Repeated contests with fatigue

1. Repeated contests with fatigue Dmitry Ryvkin Florida State University Economic Science Assocoation Meeting Rome 2007

2. Contests • Players compete for prizes by expending resources: • rent-seeking (Lockard and Tullock, 2001) • labor market contracts (Prendergast 1999, Lazear 1999) • R&D competition (Taylor 1995) • elections (Klumpp and Polborn 2005) • sports (Szymanski 2003) • Key idea: submission of the highest effort does not guarantee a win • Static model: contest success function (CSF) • Questions: choice of effort, efficiency of contracts, dissipation of rent, etc.

3. Dynamic contests • Competition may occur in several stages (rounds) • with elimination (Rosen 1986) • without elimination (Harris and Vickers 1985, 1987; Konrad and Kovenock 2005, 2006) • Examples: • patent races • “up-or-out” rules • sports • Questions: efficiency, design

4. B A Repeated contests - Competition occurs repeatedly (either continuously or in discrete “stages”) - The winner is the player who first reaches a target Continuous races (Harris and Vickers): Best-of-(2n-1) contests (Ferrall and Smith 1999; Konrad and Kovenock 2005, 2006): (0,0) (1,0) (0,1) (2,0) (0,2) (1,1) (2,1) (1,2)

5. Repeated contests • Theory: complex equilibria even for simplest stage games (Konrad and Kovenock, Harris and Vickers) • Empirical results: “burning out” • no strategic choices of effort at a given stage • no dependence of effort on the standing in the series • This work: • - Best-of-(2n-1) contests with fatigue • - An experimental study • Goals: • - See if there is strategic behavior within a given stage, and if players change their behavior depending on their standing in the series

6. The model Best-of-(2n-1) contests with fatigue Players two identical risk-neutral players repeatedly making binary choices of effort Stage game players 1, 2 choose effort levels x, y{0,1} (0=“low”, 1=“high”) probability for player 1 to win a stage contest: Fatigue net fatigue of player 1 at stage t: winning probability for player 1 at stage t: The player who is the first to win n stages wins the whole match and gets a payoff of 1. Advantage parameter Fatigue parameter

7. low (0) high (1) low (0) (1-a)/2, (1+a)/2 1/2, 1/2 high (1) (1+a)/2, (1-a)/2 1/2, 1/2 Equilibria No fatigue (f=0) a finitely repeated game with a dominant strategy Prediction: burnout Fatigue (f >0) - the stage game still has a dominant strategy (high effort) - payoffs acquire history dependence Prediction: strategic choices of effort (low effort is optimal sometimes)

8. Experimental setup This is a model-induced experiment Instructions basically explain the model using references to sports as examples Subjects: undergraduate students from Florida State University Interface: separated computer terminals, zTree (Fischbacher) Random re-matching after each match; 32 matches total (192 time periods) Treatment 4 is the no-fatigue treatment

9. Experimental hypotheses [The hypotheses are based in the model] 1. Burnout without fatigue (basic rationality, clarity of instructions) 2. More likely low effort in longer matches 3. More likely low effort for higher f 4. More likely high effort for higher a 5. More likely low effort for higher net fatigue F Key question: when subjects are aware of the presence of fatigue, will they nevertheless burn out or choose low effort at least sometimes?

10. Results I Summary statistics: % of high and low effort In treatments 1-3 % of high effort is different between low advantage/high fatigue and high advantage/low fatigue cases at less than 1% significance level. In treatment 4 the difference is rejected at 5%.

11. Regression analysis The model Results * All estimates except (*) are significant at less than 1% level

12. Conclusions • Subjects do optimize effort when they are aware of fatigue, at least in the artificial setting • Subjects’ decisions depend on their standing in the series • Extensions: • a) compare the behavior with actual equilibrium predictions; b) experiments with real tasks