Repeated contests with fatigue

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

• Players compete for prizes by expending
  resources
• rent-seeking (Lockard and Tullock, 2001)
• labor market contracts (Prendergast 1999, Lazear
  1999)
• RD 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.

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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

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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)
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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

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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 (0low, 1high) probabili
ty 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
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Equilibria
No fatigue (f0) a finitely repeated game with a
dominant strategy
Prediction burnout
Fatigue (f gt0) - the stage game still has a
dominant strategy (high effort) - payoffs
acquire history dependence Prediction strategic
choices of effort (low effort is optimal
sometimes)
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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)
Treatments low advantage/high fatigue (4 matches) high advantage/low fatigue (4 matches)
1 (n4) a 0.2, f 0.12 a 0.6, f 0.06
2 (n2) a 0.2, f 0.4 a 0.6, f 0.2
3 (n6) a 0.2, f 0.08 a 0.6, f 0.04
4 (n2) a 0.2, f 0 a 0.6, f 0
Random re-matching after each match 32 matches
total (192 time periods) Treatment 4 is the
no-fatigue treatment
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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?
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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.
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Regression analysis
The model Results

All estimates except () are significant at less
than 1 level
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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