<p>We propose an equilibrium model of behavior with Moore machines. The machines are subjected to some small likelihood of committing implementation errors. We analyze the machine game, where each player chooses in the beginning and commits thereafter to a machine to play an infinitely-repeated game. A pair of machines induces a sequence of action profiles, which are modelled by a Markov process. We derive predictions on a set of 2<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>2 games consisting of payoff variations of the Prisoner’s Dilemma, Stag Hunt and Battle of the Sexes. Crucially, predicted pairs differ across payoff variations. We also conduct experiments with a high continuation probability (specifically, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\delta =0.99\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.99</mn> </mrow> </math></EquationSource> </InlineEquation>), and contrast the frequent patterns mined from the experimental data with the equilibrium game plays and the action profiles induced by the equilibrium machine pairs. We find that almost all predicted plays and machines find support in the data.</p>

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Machine games: theory and experimental evidence

  • Christos A. Ioannou

摘要

We propose an equilibrium model of behavior with Moore machines. The machines are subjected to some small likelihood of committing implementation errors. We analyze the machine game, where each player chooses in the beginning and commits thereafter to a machine to play an infinitely-repeated game. A pair of machines induces a sequence of action profiles, which are modelled by a Markov process. We derive predictions on a set of 2 \(\times \) × 2 games consisting of payoff variations of the Prisoner’s Dilemma, Stag Hunt and Battle of the Sexes. Crucially, predicted pairs differ across payoff variations. We also conduct experiments with a high continuation probability (specifically, \(\delta =0.99\) δ = 0.99 ), and contrast the frequent patterns mined from the experimental data with the equilibrium game plays and the action profiles induced by the equilibrium machine pairs. We find that almost all predicted plays and machines find support in the data.