Christos A. Ioannou

Learning with Repeated-Game Strategies

We use the self-tuning Experience Weighted Attraction model with repeated-game strategies as a computer testbed to examine the relative frequency, speed of convergence and progression of a set of repeated-game strategies in four symmetric 2 × 2 games: Prisoners Dilemma, Battle of the Sexes, Stag-Hunt, and Chicken. In the Prisoners Dilemma game, we find that the strategy with the most occurrences is the “Grim-Trigger.” In the Battle of the Sexes game, a cooperative pair that alternates between the two pure-strategy Nash equilibria emerges as the one with the most occurrences. In the Stag-Hunt and Chicken games, the “Win-Stay, Lose-Shift” and “Grim-Trigger” strategies are the ones with the most occurrences. Overall, the pairs that converged quickly ended up at the cooperative outcomes, whereas the ones that were extremely slow to reach convergence ended up at non-cooperative outcomes.

Asymptotic behavior of strategies in the repeated prisoner’s dilemma game in the presence of errors

We examine the asymptotic behavior of a finite, but error-prone population, whose agents can choose one of ALLD (alwaysdefect), ALLC (always cooperate), or Pavlov (repeats the previous action if the opponent cooperated and changes action otherwise)to play the repeated Prisoner’s Dilemma. A novelty of the study is that it allows for three types of errors that affect agents’strategies in distinct ways: (a) implementation errors, (b) perception errors of one’s own action, and (c) perception errors of theopponent’s action. We also derive numerical results based on the payoff matrix used in the tournaments of Axelrod. Strategies’payoffs are monitored as the likelihood of committing errors increases from zero to one, which enables us to provide a taxonomyof best response strategies. We find that for some range of error levels, a unique best response (i.e. a dominant strategy) exists. Inall other, the population composition can vary based on the proportion of each strategist’s type and/or the payoffs of the matrix.Overall, our results indicate that the emergence of cooperation is considerably weak at most error levels.

Endogenous incentive contracts and efficient coordination

We examine the effects of endogenous assignment to incentive contracts on worker productivity. Assignment to high performance pay via a market mechanism is roughly twice as effective as imposing the same contract exogenously. This positive effect is largely offset by a negative effect for workers that endogenously choose low performance pay. We decompose the positive effect of endogenous assignment to high performance pay into effects due to selection and strategic anticipation, and find that selection has a greater effect than strategic anticipation. We use a Reverse Sort treatment to show that the effect of selection is sufficiently strong to overcome the direct effect of lower performance pay, yielding coordination at high effort levels in spite of low incentives.