Assume in a 2-person game that one player, Predictor (P), does not have a dominant strategy but can predict with probability p 1/2 the strategy choice of an opponent, Predictee (Q). Q chooses a strategy that maximizes her expected payoff, given that she knows p—but not P's prediction—and...

We analyze a particular episode of a popular British TV game show, “Golden Balls,” in which one of the two contestants lied about what he intended to do, which had the salutary effect of inducing both contestants to cooperate in what is normally a Prisoners' Dilemma (PD), wherein one or both...

Democracy resolves conflicts in difficult games like Prisoners' Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome....

Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently "fire" at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the...

We show that a cooperative outcome — one that is at least next-best for the players — is not a Nash equilibrium (NE) in 19 of the 57 2 x 2 strict ordinal conflict games (33%), including Prisoners’ Dilemma and Chicken. Auspiciously, in 16 of these games (84%), cooperative outcomes are...

In his classic novel, Catch-22 (1961), Joseph Heller describes a thoroughly frustrating situation faced by a combat pilot in WWII. This is generalized to a "generic" 2 x 2 strict ordinal game, in which whatever strategy the column player chooses, the best response of the row player inflicts on...

Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative...