Quotes from “Modeling Rational Players”

By Ken Binmore (1987)

The supposed paradox: that game theory necessarily requires rational players to randomize, is therefore a chimera. When a Nash equilibrium calls for the use of mixed strategies, an eductive analysis requires that the probabilities involved be seen as reflecting only the ineradicable uncertainties that a player will necessarily have about what the others will do. Jokes about game theory’s recommending that finance ministers toss coins to decide precisely when to devalue are therefore misplaced: finance ministers can achieve exactly the same effect precisely as they always have – i.e., by using a committee of economic and financial experts.#
Game theory Methodology
A definition that requires that a perfectly rational machine only be perfectly rational when playing a perfectly rational machine is circular.#
Methodology
The insistence that machines always produce an output means that their predictions will necessarily sometimes be in error regardless of the sophistication of the stopping advice.#
Rational behavior should include the capacity to exploit bad play by the opponents.#
Methodology
In chess, for example, it simply does not makes sense, given the environment in which it is normally played, to attribute bad play by an opponent to a sequence of uncorrelated random errors in implementing… Rather than resort to such a trembling-hand explanation, one would look for some systematic error in the way in which the opponent analyzes chess positions. The detection of such a systematic error will have important implications about the opponent’s expected future play, whereas the observation of a trembling-hand error will have no such implications.#
Game theory Methodology
The same formal game might receive different analyses depending on the environment from which it has been abstracted: i.e., that the analysis of a game may require more information than is classically built into the formal definition of a game.#
Game theory Methodology
[Existence] is regarded as a sine qua non for an equilibrium notion by those brought up in the Bourbaki tradition. But evolutionary stable equilibria do not always exist. Is the idea therefore to be abandoned? Clearly not. The nonexistence of such an equilibrium simply signals that the dynamics of the equilibriating process are likely to be sufficiently wild that unmodeled constraints will be rendered active.#
Methodology