This Week’s Topics

1. This Week’s Topics • Review Class Concepts • Sequential Games • Simultaneous Games • Bertrand Trap • Auctions • Review Homework • Practice Problems

2. Class Concepts – Sequential Games • Sequential Games • Decision Trees (yes, they’re back again…) • Two Payoffs: One for you, one for your opponent • Use Backward Induction to solve • Start with the outermost branches and work your way back to the root of the tree • Be careful with payouts. Now there are two to keep track of! • Remember to check which party (you or your opponent) is making the decision at each node • Key Terms • Hold Up – After one party incurs a relationship-specific sunk cost, the other party tries to renegotiate the terms. Fear of holdup can prevent deals from occurring. Reputation (for not holding up or not giving in to blackmail) can make deals possible for relationships with repeat interactions. • Entry Deterrence – An incumbent often cannot credibly claim it will fight a new entrant (since payoffs will be better without a price war). To make this empty threat credible, the incumbent can preemptively making a fixed cost investment (such as building overcapacity) that commits the incumbent to fighting. This strategic commitment to fighting will make it unprofitable for new players to consider entry.

3. Class Concepts – Sequential Games • Knowledge Check • Firm 1 must decide between two technologies (A or B) to pursue or develop. The firm has private information that A is more profitable. The projected profit of A is $70 million; the profit from B is $30 million. Firm 1 knows that after it chooses a technology, Firm 2 will either copy Firm 1 and pursue the same technology, or pursue the alternate technology. At the time of its decision, Firm 2 will know the potential profit magnitudes and which product is more profitable. If only one firm develops a technology, it obtains the entire profit. If the two firms pursue the same technology, they each obtain half the profit.

4. Class Concepts – Sequential Games • Knowledge Check

5. Class Concepts – Simultaneous Games • Simultaneous Games • Two parties with perfect information about the economic value of each outcome to themselves and their opponents. • To Solve: • Look for dominant strategies. • If you find one (or two), determine the equilibrium outcome. • If you don’t find any, continue with the next steps to look for Nash equilibrium(s). • Look for dominated strategies and remove (repeat until there are none remaining) • From the remaining strategies, find all outcomes that neither player would want to deviate from. • Key Terms • Equilibrium – An outcome where neither player could change their strategy to earn a better payoff (holding their opponent’s choice constant). The strategies of both parties and the outcome are the solution to the game • Best Response to a strategy is the choice that maximizes a player’s payoff, given that the other player is using that strategy. At equilibrium, both players chosen strategies are best responses. • Dominant Strategy – Maximizes payoffs regardless of what the other player does (the same strategy is the best response to all possible choices of the other player) • Dominated Strategy – Not a best response to any possible strategy of the other player

6. Class Concepts – Simultaneous Games • Knowledge Check • Does either player have a dominant strategy? • What are the equilibrium strategies? Equilibrium outcome? • Solution • Eliminate dominated strategy: Strategy U • Since Firm B knows that Firm A will not select Strategy U, Firm B will prefer Strategy Y (because 11>9 and 14 > 7). • Since Firm B will select Strategy Y, Firm A will prefer Strategy V. • The equilibrium solution is Strategy V and Strategy Y, with outcome (18,11)

7. Class Concepts – Simultaneous Games • Knowledge Check • Does either player have a dominant strategy? • What are the equilibrium strategies? Equilibrium outcome? • Solution • Firm A has a dominant strategy: Strategy W • Firm B will therefore choose Strategy Y or Strategy Z. • There are two equilibrium solutions • Strategy W and Strategy Y for payouts of (8,3) • Strategy W and Strategy Z for payouts of (6,3)

8. Class Concepts – Simultaneous Games • Knowledge Check • Does either player have a dominant strategy? • What are the equilibrium strategies? Equilibrium outcome? • Solution • Firm A has a dominated strategy: Strategy W • Firm B has a dominated strategy: Strategy Y • Firm A is going to always pick Strategy V • Firm B is going to always pick Strategy Z • The equilibrium solution is Strategy V and Strategy Z with payout (-4, -3)

9. Class Concepts – Bertrand Trap • Bertrand Trap • When customers care only about price (commodity product, no brand affinity, etc.) and there is more than enough capacity among firms to meet market demand, and it is a one-time interaction, firms may fall victim to the Bertrand Trap. • Both firms end up pricing at Marginal Cost.

10. Class Concepts – Auctions • Auctions • One-time auction for a single item • English Auction – Ascending bid auction. The item goes to the last party to bid. • Strategy: When to drop out • Dutch Auction – Descending bid auction. The item goes to the first party to bid. • Strategy: When to start bidding • First-Price Sealed Bid – All interested parties submit a price. The item goes to the party with the highest bid, at the price he/she submitted. • Strategy: What price to submit • Second-Price Sealed Bid – All interested parties submit a price. The item goes to the party with the highest bid, at the price of the second highest bid submitted. • Strategy: What price to submit

11. Class Concepts – Auctions • Auction Strategies and Terms • For the English Auction and Second-Price Sealed Bid – Bid your willingness to pay! • English Auction – Drop out when the bidding exceeds your WTP • Second-Price Sealed Bid – Write down and submit your WTP • For the Dutch Auction and First-Price Sealed Bid – Bid below your willingness to pay! • There is no dominant strategy • Your strategy depends on what you believe your competitors are willing to pay • If all bidders are risk neutral then all four bidding rules produce the same expected revenue to the seller. • Private Value – Your value of the item up for auction is independent of the value to others. (For Dutch & First-Price Sealed Bid, more biddersshade less) • Common Value – There is an actual value to the item, which is estimated by all participants. (More biddersshade more)