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8: A general expression and graph showing effort for symmetric Nash equilibrium with different values of risk for CRRA utility function. On X-axis is the r (risk preference) and Y-axis is the optimal effort.

8: A general expression and graph showing effort for symmetric Nash equilibrium with different values of risk for CRRA utility function. On X-axis is the r (risk preference) and Y-axis is the optimal effort.

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We study contests as an example of winner-take-all competition with linearly ordered large strategy space. We study a model in which each player optimizes the probability of winning above some subjective threshold. The environment we consider is that of limited information where agents play the game repeatedly and know their own efforts and outcome...

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Context 1
... agents are playing as per contest reaction function based on forming beliefs on other agents' effort, then the direction of dropout (if at all) should be preceded by a decrease in effort, not an increase in effort as more often observed in the data. The agent should not put in any effort more than the prize value divided by the number of agents, for a risk-neutral case (Figure 2.6). ...
Context 2
... broadly speaking, being more risk-averse means less effort and risk-seeking means higher effort. In Figure 2.8 below, the general equation for symmetric NE with risk as a parameter and its graph is provided for the case when agents have a CRRA utility function. ...
Context 3
... objective of the simulation exercise is to see if it can track the aggregate data and understand the possible trajectories for various values of the parameters (Fig 2.15-2.17 in Appendix). Given the probabilistic nature of the game and the difficulty of estimating the parameters of an individual player, the periodwise comparison of the actual behavior of an agent in the experimental data with the artificial agent in the simulation cannot be made. ...

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