Experiments with cooperative 2 × 2 games

Abstract

Nash's solution of a two-person cooperative game prescribes a coordinated mixed strategy solution involving Pareto-optimal outcomes of the game. Testing this normative solution experimentally presents problems in as much as rather detailed explanations must be given to the subjects of the meaning of ‘threat strategy’, ‘strategy mixture’, ‘expected payoff’, etc. To the extent that it is desired to test the solution using ‘naive’ subjects, the problem arises of imparting to them a minimal level of understanding about the issue involved in the game without actually suggesting the solution.

Experiments were performed to test the properties of the solution of a cooperative two-person game as these are embodied in three of Nash's four axioms: Symmetry, Pareto-optimality, and Invariance with respect to positive linear transformations. Of these, the last was definitely discorroborated, suggesting that interpersonal comparison of utilities plays an important part in the negotiations.

Some evidence was also found for a conjecture generated by previous experiments, namely that an externally imposed threat (penalty for non-cooperation) tends to bring the players ‘closer together’ than the threats generated by the subjects themselves in the process of negotiation.