Bounded Versus Unbounded Rationality: The Tyranny of the Weak

Itzhak Gilboa (1) , Dov Samet (1, 2)

1 Northwestern University [Evanston]
2 TAU - Tel Aviv University

We examine the case of a two-person repeated game played by a boundedly rational player versus an unboundedly rational opponent. The former is restricted to strategies which are implementable by connected finite automata. It is shown that the "rational" player has a dominant strategy, and that in some cases the "weaker" (boundedly rational) player may exploit this fact to "blackmail" him. It is also shown that for a repeated zero-sum game, the rational player has a strategy which drives the automaton player's limit payoff down to his security (maxmin) level, even if he may choose any finite automaton.

Keywords: Bounded; Unbounded Rationality; Tyranny of the Weak

Domains: Economy and decision science

Itzhak Gilboa, Dov Samet. Bounded Versus Unbounded Rationality: The Tyranny of the Weak. Games and Economic Behavior, 1989, vol. 1, pp. 213-221. ⟨10.1016/0899-8256(89)90009-2⟩. ⟨hal-00753239⟩