Equilibrium play in matches: Binary Markov games

The Value of a Draw in Quasi-binary Matches

A match is a recursive zero-sum game with three possible outcomes: player 1 wins, player 2 wins or there is a draw. Play proceeds by steps from state to state. In each state players play a “point game” and move to the next state according to transition probabilities jointly determined by their actions. We focus on quasi-binary matches which are those whose point games also have three possible o...

A hidden Markov model for the detection of pure and mixed strategy play in games∗

We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that al...

Reinfor ement Learning to Play An Optimal Nash Equilibrium in Team Markov Games

Nash equilibrium in strictly competitive games: live play in soccer

I model a scoring situation that arises frequently during soccer matches. The Nash equilibrium solution is shown to be broadly consistent with the conventional wisdom of experts. Data on goals scored over an entire season in Italy’s soccer league provide statistical support for a prediction of the model’s Nash equilibrium. D 2004 Elsevier B.V. All rights reserved.

On Asynchronicity of Moves and Coordination∗

This paper shows that asynchronicity of moves can lead to a unique prediction in coordination games, in an infinite-horizon setting, under certain conditions on off-equilibrium payoffs. In two-player games we derive necessary and sufficient conditions for play ultimately being absorbed in the Pareto dominant Nash equilibrium of the stage game, for every Markov perfect equilibrium. For players p...