Explaining strategic coordination: Cognitive hierarchy theory, strong Stackelberg reasoning, and team reasoning.

Andrew M Colman,Catherine L Lawrence,Briony D Pulford

doi:10.1037/dec0000001

Abstract

In common interest games, players generally manage to coordinate their actions on mutually optimal outcomes, but orthodox game theory provides no reason for them to play their individual parts in these seemingly obvious solutions and no justification for choosing the corresponding strategies. A number of theories have been suggested to explain coordination, among the most prominent being versions of cognitive hierarchy theory, theories of team reasoning, and social projection theory (in symmetric games). Each of these theories provides a plausible explanation but is theoretically problematic. An improved theory of strong Stackelberg reasoning avoids these problems and explains coordination among players who care about their co-players’ payoffs and who act as though their co-players can anticipate their choices. Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation. Cognitive hierarchy Level-1 reasoning, facilitated by a heuristic of avoiding the worst payoff, tended to predominate, especially in more complicated games, but strong Stackelberg reasoning occurred quite frequently in the simpler games and team reasoning in both the simpler and the more complicated games. Most players considered two or more of these reasoning processes before choosing their strategies.

Highlights

As Schelling (1960, chap. 3) was the first to demonstrate empirically, human decision makers are remarkably adept at coordinating their actions and their expectations of one another’s actions, but it is surprisingly difficult to explain how they achieve this
General Discussion Results of the experiments reported here are highly consistent with each other, and they suggest that cognitive hierarchy Level-1 reasoning, strong Stackelberg reasoning, and team reasoning each played a part in explaining players’ strategy choices in 3 × 3 and 4 × 4 experimental games
Cognitive hierarchy Level-1 reasoning was most influential, especially in 4 × 4 games, but strong Stackelberg reasoning was influential in 3 × 3 games, and team reasoning in both 3 × 3 and 4 × 4 games

Summary

Introduction

As Schelling (1960, chap. 3) was the first to demonstrate empirically, human decision makers are remarkably adept at coordinating their actions and their expectations of one another’s actions, but it is surprisingly difficult to explain how they achieve this. Let us assume that the partners have not discussed the service but are twice as likely to win the point if both choose the wide rather than the center option and have no chance of winning the point if they choose different options, given the particular circumstances at the time If both players know all this, they are involved in a coordination problem with a strategic structure corresponding to the Hi-Lo game shown, where wide corresponds to H and center to L. It seems intuitively obvious that rational players will choose H in the Hi-Lo game, resulting in the payoffdominant outcome (H, H), and it is surprising that game theory provides a player with no reason or justification for choosing H To see why this is so, consider the following standard common knowledge and rationality assumptions of game theory: 1. The players are instrumentally rational in the sense of always choosing strategies that maximize their own individual payoffs, relative to their knowledge and beliefs, and this too is common knowledge in the game

Methods

Findings

Conclusion