Random Actions in Experimental Zero-Sum Games

Jung S You

doi:10.22610/jebs.v13i1(j).3150

Abstract

A mixed strategy, a strategy of unpredictable actions, is applicable to business, politics, and sports. Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions. I test i.i.d. hypotheses of the mixed strategy Nash equilibrium with the simplest experiments in which student participants play zero-sum games in multiple iterations and possibly figure out the optimal mixed strategy (equilibrium) through the games. My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game). The results indicate the need to further develop theoretical models that explain a non-Nash equilibrium behavior.

Highlights

A mixed strategy is a strategy in which a player randomly takes actions from a set of available actions, based on a set of calculated probabilities (Pindyck & Rubinfeld, 2014)
The first null hypothesis that the mixed probabilities for individual players are identical across pure strategies in each repetition of symmetric zero-sum games is rejected at a 10% significance level for all 72 participants except four players under the matching-pennies game
My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest matching-pennies and rock-paper-scissors games

Summary

Introduction

A mixed strategy is a strategy in which a player randomly takes actions from a set of available actions, based on a set of calculated probabilities (Pindyck & Rubinfeld, 2014). I investigate how closely the mixed strategy Nash equilibrium theory can predict individual behavior in finitely repeated zero-sum games: matching-pennies and rock-paper-scissors. The payoff in matching-pennies and rock-paper-scissors includes only two outcomes of wins and losses; the games are symmetric with respect to the mixed strategies of the row and column players and gameplay is face-to-face Due to their simplicity in structure and equilibrium solution, players face a cognitively less demanding task than those in other experiments. The first null hypothesis that the mixed probabilities for individual players are identical across pure strategies in each repetition of symmetric zero-sum games is rejected at a 10% significance level for all 72 participants except four players under the matching-pennies game.

Zero-Sum Game Experiments

Empirical Analysis

Findings

Conclusion