Abstract
Howard's (1966) formal solution for the Prisoner's Dilemma is based upon a concept of “metagame” which allows several levels of conditional strategies. If player B reacts to player A's strategies, this forms BG metagame. In metagame BG, outcome (d, d/d) is the only equilibrium, where x/y=x if A chooses c, and x/y=y if A chooses d, and it yields (d, d) in the basic game G. If A reacts to B's reactions to A's strategy choices, this forms ABG metagame. In metagame ABG, both (c, c) and (d, d) are metaequilibria, and possible stable outcomes in G.
The purpose of this study is to examine the possible reactions of subject (player A) to hypothetical player B's possible strategy choices, and to evaluate the metagame theoretic assertions.
One hundred and fifty-nine subjects are randomly assigned to one of the five payoff matrices. In each payoff condition, subjects were told to react by choosing c or d to a basic game G situation, four metagame AG situations, and four expanded metagame ABG situations, which are represented in questionaires.
The main results can be summarized as follows:
(1) In a basic game G situation and all four metagame AG situations, nearly all subjects have no hesitation in choosing d regardless of payoff matrices.
(2) In expanded metagame ABG situations, if and only if hypothetical player B chooses c/d, many of the subjects choose c and more than half of them expect that outcome (c, c) is stable regardless of payoff matrices.
These results sugest that mutual expectations, defined as reciprocal expectations that go on to higher-order, are essential for agents to coordinate their actions.
