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Conceptual Classification of Games: Dichotomy of strategic interaction: pure type

1. Information and Game Theory 1.2 Strategic Games. Conceptual Classification of Games: Dichotomy of strategic interaction: pure type Ex) When to take action?; Sequential moves(ex: chess) OR simultaneous moves(ex: Rock-paper-scissors)

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Conceptual Classification of Games: Dichotomy of strategic interaction: pure type

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  1. 1. Information and Game Theory1.2 Strategic Games • Conceptual Classification of Games: Dichotomy of strategic interaction: pure type • Ex) When to take action?; Sequential moves(ex: chess) OR simultaneous moves(ex: Rock-paper-scissors) • Ex) Once (one-shot game with someone you will never meet again) OR repeated (with someone you will play the game over and over again)? • In practice, pure type games are rare. Games are mixed with two or more types. However, we can deal with many mixed types by studying the pure types

  2. 1. Information and Game Theory1.2 Strategic Games • Basic concepts and jargons • Application of game theory • Structure of game theory • Rules of the Game = Mechanism; 게임상황이라고 판단되는 경우 고려하여야 하는 요소들. • Players(선수) • Strategies(전략) • Payoffs(보상) • Equilibrium(균형) a move Action 1 3-8-19 Action 2 Action 3 *a move: a single action taken by a player at a node (?): 여러액션을 취할 수 있는 특정상황 ex) It’s your move. *a strategy: a complete plan of actions  action ⊂ move ⊂ strategy

  3. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game • Conventional Decision Theory: When making, do not consider how people would react to the decision or what impact the decision would have on others. However, decisions/actions interact. Ex) If you study harder in this class, your friends will get worse grade. If this fact is not detected by any players, this isn’t a game situation (no interactions). • Game Theory: For these interactions to be a strategic game, participants need to be aware of the interactions. Ex) The fact that I know about this interactions needs to be known by the other players and the fact that this is common knowledge needs to be known by others and so forth…

  4. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game (cont’d) • The less mature, the less recognize these interactions.(관계지능) Thus, immature people play less games. Ex) Less attention to the daily news when younger. • Thus, a simple game of dice play(other players’ willful actions do not influence my result. Pure chance.) or game of cube puzzle(pure skill, playing alone) are not the subjects of this lecture. • If there is NO interaction among players or players are not aware of the interactions, these games are not ‘games’ as defined in this lecture. Then what are the games to consider in this lecture? • Ex. of strategic games: Soccer, The 6-party Talks for North Korea’s nuclear weapon, labor problems and negotiation.

  5. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game (cont’d) • How about economic games in agriculture? : Until recently, not regarded as a game b/c many providers and consumers  individual decisions do not affect others’ decision or whole economy  impersonal law of demand/supply decides the price. • That is, because there are too many people, players are not sure with whom they are playing. Therefore, not a game situation? YES; these are games too. Ex)Collective Action Game. More details in the next slide. • Aside: Are we playing games with God? Do we know what God’s will(strategies) is? Is a boy, playing with a bug, playing a game with the bug? In Korean, 게임이 안돼… (no match for the game)

  6. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game (cont’d) • In many cases, a game with thousands of players tends be reduced to 2-person game or to a game of small number of players throughmutual commitment (Ex. Marriages. There are many fish in the sea but, alas, monogamyprevails…) or private information. • Ex. of mutual commitment: When building a house, there are hundreds of contractors. But after choosing one and making a contract, the relationship becomes bilateral. It becomes a game between the contractor who wants to finish the job with less cost fast and the owner who want to block contractor’s moral hazard using contract terms-and-pay-method for the remainder(잔금).

  7. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game (cont’d) • Ex. of private information: Thousands of farmers who want loans VS. hundreds of banks  Farmers with competitive advantages in farming techniques have better chance to pay back Individual farmer appeal for his/her competence (only s/he knows if s/he is competent; private information); Banks try to screen; Thus, a 2-person game between a bank and a farmer. Another example: health insurance. Only the insured know the exact health condition. • My intention to make a girlfriend is private information. You only tell the one girl or very close friends. If you try to have 2 girl friends simultaneously? You become a menace to the society. The dating is usually a 2 person game. Casanova? Casanova

  8. 1. Information and Game Theory1.2 Strategic Games 1.2.1 Decision Making vs. Game (cont’d) • Why shopping at WWW is cheaper? • Invisible Hand theory: There are usually more supply than demand on the internet. True? No. Actually there are more shoppers than shopping malls on the internet.  can’t explain the new phenomena. • Game theory: Consumers’ information on seller and prices ≫(superior) Sellers’ information on consumers. Disclosing consumers’ private information, using screening device, on the internet is harder than face-to-face sales. lower prices • Thus, Game Theory explains better than the Invisible Hands of Adam Smith(classical supply & demand model); GT is more advanced and more comprehensive.

  9. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game Games will be classified with two extreme criteria and rests are considered as mixture of the two. 1) Are moves sequential or simultaneous? • Sequential move: chess, go(바둑); Once I take this move, what move the opponent would take next?  dynamic game (but time is less relevant, info. is) • Simultaneous move: sealed bid, rock-paper-scissors; What if I do this and my opponent do that at the same time?  static game

  10. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) • Even though classifiable with two criteria, most games are mix of the two. Ex) American football. The coach gives direction on how to attack, expecting opponent’s move(without knowing how the opponent will move) but when the opponent’s move is not as expected, the quarter back can change moves. (first static, later dynamic game) • Moving first is always advantageous? NO. Usually, in many competitions, moving first may be advantageous. (ex: introducing new product before others so that other companies can’t enter the market; first mover advantage) • However, in many political-election games, second mover has advantage b/c s/he can observe what moves the opponent took so that s/he can make adjustment in the move. (ex, 2016-17 국정농단, 대통령측 공소장 보고 대응전략 짜기)

  11. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 2) Zero-sum(or more generally, constant sum) OR Non-zero-sum? • zero-sum game : If I win, you (the opponent) lose(win-lose). My gain is your loss. when players’ interests are in total conflict. Ex) Chess, gambling, soccer. • non-zero-sum game : Most of economic/social games. win-win or lose-lose games. But still fight for who gets more or less. Ex) nuclear war; both are losers(lose-lose game). Loser’s loss is not gain of the winner. Ex) Price war. Labor conflict.

  12. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 3) one-shot or repeated? (static or dynamic game과 다름), With the same opponent or different opponent? • One-shot game: No need to consider future effects or reputation. tends to be ruthlessly played. Lack of information on others  blocking information or surprise attack can be very effective. Ex) Fruit seller on street. • Repeated games: Reputation(ruthlessness, fairness, honesty, credibility) is important. Cooperation for each other’s interest is very plausible; promise to alternate victory  if not kept, punishment(eye for an eye, tit-for-tat; equivalent retaliation; very effective strategy). *tit, tat : 가볍게 때림

  13. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 3) one-shot or repeated?(cont’d) • Even zero-sum game in the short-run can become non-zero-sum(win-win) game in the long run. • Ex) Drafting in professional sports; In the short-run, winning always is good for Team A. But if Team A wins all the time, spectators will lose interest.  draft: lowest rank team (Team Z) gets to choose players first  All teams become equally competent  games get unpredictable  more interesting  more spectators, more money to every team.

  14. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 3) one-shot or repeated?(cont’d) • If too aggressive, it may be advantageous in the short run but in the long-run, it will be disadvantageous; better to form an alliance. Moving with the herd. • You will be surprised to see how effective the honesty/fairness or Golden Rule is.(Golden Rule: Do unto others as you would have them do unto you.)

  15. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? • Do they have full information (on others’ strategies)? In chess, both players have full information on current situation, all the moves so far and the each other’s intention to win  this rare situation is expressed as ‘players have perfect information.’ • Perfect (Strategy)vs. Complete (payoff) • In most games, they have limited information  imperfect information; details in chapter 2 • Ex) External variables such as weather, no information on new opponent.

  16. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? (cont’d) • Do they have equal information (on others’ payoffs)? Incomplete information OR asymmetric information: When one player has more information or private information. • Ex) Used car salesman : Has more info on the quality of the used car than the buyer. has incentive to sell poor quality car at higher price (adverse selection(역선택); the effect of asymmetric info occurs before transaction) *organic food market, Korean beef market, etc. • Why called ‘adverse’ selection (anti-selection, negative selection)?the "bad" products or sellers are more likely to be selected (Wiki))

  17. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? (cont’d) • Policyholders: Once insured, they tend to loosen up for health management. (moral hazard(도덕적해이); the effect of asymmetric information occurs after transaction) • Ex) Central heating/cooling  Let the fan keep operating even though it is warm or cool enough b/c they don’t pay more or less.  energy wasted. • Adverse selection or moral hazard are both effects of asymmetric information, though. *hazard: 위험, 모험, 위험요소(원인), 해악 3-13-19

  18. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? (cont’d) • Perfect: as good as it could possibly be.  qualitativestandard • Complete: as great in extent, degree, or amount as it possibly can be.  quantitative standard • whole: all of it. • Definitions in dictionary are similar. But in game theory, they are differentiated. • Loosely speaking, * [if you don’t know the other player’s payoff function, you have incomplete information.] * [If you don’t know the other player’s strategy, you have imperfect information.] Details later.

  19. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? (cont’d) • Is it better to conceal your superior information? YES and NO. • YES: Ex) It is more advantageous for US that Iraqis don’t know the Pentagon is watching over the sky how they move. War. • NO: Ex 1) Pharmaceutical company. Developing new drug  need to let the word out so that other competing company stops developing the same drug. Ex 2) diplomacy: let the other countries know her peaceful (or hostile) intentions as in North Korea’s nuclear experiment. • Selectively leak information when it is advantageous.

  20. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 4) Do players have full or equal information? (cont’d) • What if the other player thinks that your exposed information is false or exaggerated? 絶大내숭(內凶; 내흉?) Manipulation of Info. • Signaling: strategy for the player with more information to prove that the information is a fact. • Screening: strategy for the player with less information to make the other player reveal the truth. Ex) commitment game • Manipulation of information itself becomes a game and it becomes more important than the actual game.

  21. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 5) Is the rule of the game fixed or manipulable? • Fixed rule games: chess, cards, sports • Manipulable rule games: business, politics, life in general  players can make their own rules and manipulate • Ex 1) Parents continuously make rules and children always try to manipulate or avoid the rules. • Ex 2) Oder of voting for each issue at Congress is important and manipulable. Why order is important? Ex) Soccer tournament. If the winning probabilities of 3 teams are as follows A>B, B>C, C>A, case 1) B vs. C  B; A vs. BA wins; case 2) C vs. A  C; C vs. B B wins. Order is important. Poker Face: Show no feelings

  22. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 5) Is the rule of the game fixed or manipulable? • In these cases, making rules itself is a game.(pre-game, 사전게임). • Lobbying activities are very important to businessmen. • Other examples) WTO negotiations, fair trade acts(공정거래법), World-Cup match list.

  23. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) Love binds? 6) Is the agreement enforceable?  cooperative vs. non-cooperative • If there exists an enforceable mechanism such as law, institutional or social system to punish the non-compliant of the agreement, the game is called cooperative(공조적) game. Otherwise, called non-cooperative(비공조적) game. • If the level of punishment is harsh enough (binding), they will comply. Is marriage a cooperative game? YES in Korea before. No in many other countries. In Korea, adultery was a criminal offense… not any longer! • One of outcome concepts in the cooperative game: Core: the outcome of a game that no players can find better alternatives.

  24. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) • Babylonian Talmud(BC 24C) : A man owes debts of 100, 200, and 300, but dies with insufficient funds to pay everyone.  suggests a division rule for property of deceased debtor  coincides with theNucleolus(中核; center of the core; 1985, Aumann and Maschler). Game theory is very old. • Waldegrave (1713); Cournot (1838); Edgeworth (1881); idea of game theory found. • After von Neumann and Morgenstern, (1944), Theory of Games and Economics Behavior  modern game theory emerges. Bargaining powers are assumed to be the same. If X1<X2 AND X1<X3, core? (50, 75, 75), …, (60, 70, 70), …, (66, 67, 67) 동일 배분 ? 중핵!! 부채비율로 배분

  25. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) Estate is 100 Estate is 200 Estate is 300 Creditorof 300 Creditorof 300 Creditorof 300 300 300 300 200 200 200 100 100 100 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300 300 300 Creditorof 200 Creditorof 200 Creditorof 200 Creditorof 100 Creditorof 100 Creditorof 100 Core: 노란색 평면 Nucleolus: (33.33, 33.33, 33.33) (50, 75, 75) (50, 100, 150) 중핵: 도형의 무게중심 4개 삼각형 면적 동일

  26. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) Skip Howto calculate the Nucleolus when the estate is 200? • Locate the center of the mass of the core. • The center should be located on the dotted line inthe right figure because the polygon is symmetric. • Then the coordinate for the creditor of 100 at the center should be 50. We also know the credits that the creditor of 200 and the creditor of 300 can get are the same on the dotted line. Let it be X. • But we know the total credit the 3 can divide is 200. Thus, the following equation should hold at the center. 50 + 2*X = 200. Thus, X=75. • Finally, therefore, the Nucleolus is (50, 75, 75). The Core when the Estate is 200. a h b S=0.5*(a+b)*h

  27. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 6) Is the agreement enforceable?  cooperative vs. non-cooperative (cont’d) • However, many games are non-cooperative; International agreement? No effective enforcement mechanism  Ex 1) Can’t control North Korea. War? Not an option. Ex 2) private information Ex 3) cost of enforcement ≫ benefit of enforcement  enforcement mechanism doesn’t work. non-cooperative game. • In many Korean books, cooperative games are translated as ‘협조적게임,’ Non-cooperative games are translated as ‘비협조적게임.’ However, in this course, we will call them ‘공조적게임’ and ‘비공조적게임,’ to emphasize the importance of interaction and cooperation effects.

  28. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 6) Is the agreement enforceable?  cooperative vs. non-cooperative (cont’d) • non-cooperative gamecan’t bring forthcooperative results? YES, we can have cooperative results! • Interesting result of game theory is that cooperative results can be derived from non-cooperative behaviors of the players.  Repeated games, collective action games, evolutionary games)

  29. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 6) Is the agreement enforceable?  cooperative vs. non-cooperative (cont’d) • non-cooperative game: focus on individual actions (process) • cooperative game : focus on group actions (result; the eq. should be fair to be stable) • This semester, we mostly talk aboutnon-cooperative games. Next semester, in the ‘Bargaining Theory in Agriculture,’ we will deal with cooperative games. Distribution Justice Distribution Efficiency Cooperative games Game Theory Information Asymmetry Static-Dynamic Zero-sum, Non-zero-sum Number of strategies, etc Non-cooperative games

  30. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 7) Number of Strategies and Continuity of Strategies • If there are unlimited number of strategies, the game is called as ‘infinite game’. If limited, called as finite game. • If the strategies are continuous, the game is called as ‘continuous game.’ If not continuous, discrete games (離散게임, 불연속게임). *discontinuity (irregular) • Generally speaking, limited games are discrete games and unlimited games are continuous games. There are exceptions, however. semi-continuous (upper) discontinuous discrete

  31. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 7) Number of Strategies and Continuity of Strategies • Discrete-Unlimited games: -∞<price in integer<+ ∞ • Discrete-Limited games : 100< price in integer <200 • Continuous-Unlimited games: 101<price in infinite decimal<102 • Continuous-Limited games? Not defined with the definitions so far. More details later. -∞ + ∞ price in infinite decimal 100 150 160 200 100 200 101 102

  32. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 8) How to express games? • Normal Form(정규형)/Strategic Form(전략형) and Extensive Form(확장형) • NormalForm: payoff tables, suitable for analysis of static games • Extensive Form: game tree, suitable for analysis of dynamic games • However, both can be expressed by another form.

  33. 1. Information and Game Theory1.2 Strategic Games 1.2.2 Classification of Game (cont’d) 8) How to express games? (cont’d) • Normal Form(정규형) • Extensive Form (확장형) Player3 takes Strategy 1 Player3 takes Strategy 2 Moves ≈ Strategy Player2 Player1 Strategy = ∑plan of moves Move = ∑plan of actions Nature action Strategy = ∑ Moves action

  34. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions 1) Strategies • Strategy(전략): Alternative moves given to the players(limited, unlimited, continuous, discrete). • More comprehensively, a complete plan of actions. *tactic(전술): smaller scale, shorter term. The term ‘tactic’ is not used in game theory. • How do we know if a plan is complete?  A strategy is complete when it doesn’t matter if I execute the strategy myself or give the direction to someone else in accomplishing the same result.

  35. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 2) Payoffs • When playing games, it is more important to maximize your prize rather than to win. The prize is called the payoff. The bigger, then better. If the payoff when you lose is bigger than the payoff when you try to win, you are better-off losing. • Ex) ranking or money, market share, ratings(시청률)… • 행동경제학: 실험을 통해 보니… 사람들이 경제적 보상에 의해서만 움직이지 않는다… 심리학+경제학 • 게임에서 보상은 경제적보상+심리적보상. 단, 심리적 보상도 정량화 되어야 함

  36. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 2) Payoff (cont’d) Two important assumptions • Payoff includes all the interests of the players. If the player is altruistic and feels happy to help others, this should be reflected in the payoff. Ex) If the player is happy to lose to the opponent, this happiness should be transformed in monetary or quantitative terms and reflected in the payoff. • If the payoff is given by chances, the payoff is (weighted) average. Ex) The prob. to win 0 is 75% and the prob. to win 100 is 25%, the payoff is 25(= 0*0.75 + 100*0.25). This is, in particular, called ‘the expected payoff.’ • Additional assumption: Players are neutral to the expected payoffs of 25(=0*75%+100*25%) and 25 (=25*100%; 25 for sure)  risk neutral(위험중립적)

  37. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 2) Payoff(cont’d) • 25*100% ≫ [0*75%+100*25%]; risk averse 25*100% = [0*75%+100*25%]; risk neutral25*100% ≪ [0*75%+100*25%]; risk loving • Most people are risk averse and prefer 25 for sure (25*100%≫ [0*75%+100*25%]; We can deal with this using non-linear transformation(more details later). • However, you can’t succeed without taking risks. Of course… Ex) 8 people are to divide $200. The 4 people in the group: 1 took the risk and only one earned $100 and other 3 earned nothing. The other 4 in group 2 didn’t even tried but earned $25 each.  unequal distribution of wealth  can’t earn more than $25 without taking risks. Younger people are more advantageous b/c they have more chance down the road.; The Parable of the Talents(Mathews 25:14-30).

  38. The Parable of the Talents (Matthew 25:14-30; Luke 19:12-28) 2+2=4 1+0=1 • 13 “Therefore stay alert, because you do not know the day or the hour. 14 For it is like a man going on a journey, who summoned his slaves and entrusted his property to them. 15 To one he gave five talents, to another two, and to another one, each according to his ability. Then he went on his journey. 16 The one who had received five talents went off right away and put his money to work and gained five more. 17 In the same way, the one who had two gained two more. 18 But the one who had received one talent went out and dug a hole in the ground and hid his master’s money in it. 19 After a long time, the master of those slaves came and settled his accounts with them. 20 The one who had received the five talents came and brought five more, saying, ‘Sir, you entrusted me with five talents. See, I have gained five more.’ 21 His master answered, ‘Well done, good and faithful slave! You have been faithful in a few things. I will put you in charge of many things. Enter into the joy of your master.’ 22 The one with the two talents also came and said, ‘Sir, you entrusted two talents to me. See, I have gained two more.’ 23 His master answered, ‘Well done, good and faithful slave! You have been faithful with a few things. I will put you in charge of many things. Enter into the joy of your master.’ 24 Then the one who had received the one talent came and said, ‘Sir, I knew that you were a hard man, harvesting where you did not sow, and gathering where you did not scatter seed, 25 so I was afraid, and I went and hid your talent in the ground. See, you have what is yours.’ 26 But his master answered, ‘Evil and lazy slave! So you knew that I harvest where I didn’t sow and gather where I didn’t scatter? 27 Then you should have deposited my money with the bankers, and on my return I would have received my money back with interest! 28 Therefore take the talent from him and give it to the one who has ten. 29 For the one who has will be given more, and he will have more than enough. But the one who does not have, even what he has will be taken from him. 30 And throw that worthless slave into the outer darkness, where there will be weeping and gnashing of teeth’” (Matthew 25:13-30). 5+5=10

  39. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 3) Rationality (of participating players) • Rationality assumption: Players are completely able to calculate their payoffs + to assign preference on all possible outcomes of the game. • Rational players do not need to be short-sighted/selfish. They do not need to have the same value systems with others nor to be ethical/moral. However, the rational person needs to maintain his/her value system consistently. • Most human relationships are games. Thus, people who get blames are not the ones who have different opinions but who are not consistent, specially in the longer term.

  40. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 3) Rationality (cont’d) • Thus, even when it is rational to yourself, it can seem to be irrational to others. • Ex) Iraq War: Western leaders and Hussein may have different value systems. Thus, Hussein may not take strategies that the western leaders think rational. Same with the North Korean nuclear problems. In the Middle East, males’ testimony is twice more accountable than females’. From the view point of western world, this it may not seem rational. However, if the consistency holds, this is rational to Middle East world from the view point of game theory. • Generally, each player does not know others’ value system (incomplete and asymmetric information). How to figure out others value system (or to hide mine) is a very important strategy.

  41. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 3) Rationality (cont’d) • Are these assumptions realistic? At a glance, NO. People do not know even their own value system for sure. Even though they know, it is impossible to make up all the possible list of alternatives and rank the preferences on the alternatives. Ex) Chess. It is possible to calculate all the expected moves in theory. However, there are so many possible moves that no one or computer even completed the calculation yet. It is more like an art. • Then, is the game theory useless? When you play similar games often, the above assumptions become reality. Without a complete calculation, similar outcomes are to emerge. Proofs from experimental economics support this fact. 3-15-19

  42. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 3) Rationality (cont’d) • Ex) If you live long enough with your spouse, you will learn about your spouse’s value system. Or intensive research can do the same job. Or you can use screening device to figure out what kind of value system the other has.  충돌하는 가치관의 예: 남자의 동거=결혼 vs. 여자의 동거≠결혼 • A thoroughly prepared strategy for all possible contingencies can minimize your mistakes that can be abused by the opponents against your advantage. The opposite possibility also exists. Thus, it is safer to assume that the other players are rational as well. That is, assuming what others can do (capabilities) is safer than assuming what others can’t do(limitations).

  43. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 4) Common knowledge of rules • Rules of the game 1. List of the players 2. Possible strategies of each player 3. All possible payoffs 4. Rationality assumption (equilibrium) • All participating players should be aware of these rules and the fact that the other player is aware of these rules should be recognized by the opponent, and the fact that the fact is known to the other player has to be recognized by the other and all these, again, has to known to everybody and all these are…  common knowledge (상식)

  44. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 4) Common knowledge of rules (cont’d) • Game theory can’t be used if any of the above rules is missing. However, as we know that surprise attack is more effective, if the opponent is not aware of my strategy or if I use a strategy that is never expected by the opponent, I tend to win. Then, is game theory useless? (b/c we need all possible strategies) • We can assign probability on a very implausible alternative if it can happen at all. We will consider these kind of games in asymmetric information games (Bayesian Games). • Whatever can happen will happen (Murphy’s Law) • What should happen will happen (Amartya Sen’s Law)

  45. Equilibrium 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) No Eq. 5) Equilibrium • Interaction among rational players  can expect equilibria. If all players are playing their best strategies (responses) and have no more incentive to change their strategies, this equilibrium is called ‘Nash Eq.(equilibrium).’ • An eq. is stable once reached? NO. Eq. is always superior to other alternatives? NO. • Finding eq. is harder than defining eq. • With pencil and paper, a game for 2-3 players with 3-4 strategies are solvable. More than that? Not practical to solve it by hand.

  46. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 5) Equilibrium (cont’d) • How to find an eq. for complex games? Humans are not patient enough to do the repeated calculations? Use Mathematica, Gambit. • Then why study simple games? To understand the outcomes from the computer and use/interpret them. Ex) If we understand addition, subtraction, multiplication, division rules, we don’t need to check if the Excel did the right calculation • Ex) 3 + 4 x 5 = 3 + (4 x 5) = (3 + 4) x 5 ??

  47. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 6) Repeated games and Evolutionary games • Games among beginners, b/c they lack understanding, may result in different outcomes from the expected outcomes of game theory. • However, through learning process, the outcomes will converge continuously.  This is dealt with Evolutionary games; successful(superior) players survive, inferior players will extinct eventually. This is called an ‘evolutionary stable state(ESS).’ Even though players are not aware of the game situation, the result tends to coincide with the result of games among rational players.

  48. 1. Information and Game Theory1.2 Strategic Games 1.2.3 Terms and Assumptions (cont’d) 7) Observation and Experiment • So far, we focused on how to think about games or how to analyze the strategic interaction  mostly on theory. • Theory and Reality: Reality helps to construct theory and to validate the theoretical result. • How? 1) Observation of reality on natural setting 2) Artificial experiment • Result? Sometimes theory coincides with reality, sometimes, it doesn’t. Ex) Supply-Demand game (coincides). Prisoners’ dilemma (does not coincides, cooperate). More details later.

  49. 1. Information and Game Theory1.2 Strategic Games 1.2.4 Application of Game Theory • How to apply game theory? • Explanation: why did this phenomena occur? • Prediction: What result is expected? • Consulting and prescription: What kind of strategies need to be deployed? • Studying theory may not able to remove all the discrepancies btwn theory and reality but can reduce the magnitude.

  50. 1. Information and Game Theory1.2 Strategic Games 1.2.5 Lecture Plans • This semester deals with non-cooperative games only.  4 big chapters. Chapters 2-1/2/3/4 Chapter 4-2 Chapter 3-1 Chapter 4-3 Chapter 3-2

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