Rationality and Coherent Theories of Strategic Behavior

Abstract

A non-equilibrium model of rational strategic behavior that can be viewed as a refinement of (normal form) rationalizability is developed for both normal form and extensive form games. This solution concept is called a τ -theory and is used to analyze the main concerns of the Nash equilibrium refinements literature such as dominance, iterative dominance, extensive form rationality, invariance, and backward induction. The relationship between τ -theories and dynamic learning is investigated.JEL classification number C72

Chess-like Games Are Dominance Solvable in at Most Two Steps

“…Cf., e.g., Samuelson (1992), Börgers and Samuelson (1992), Ewerhart (1998), and the discussion in Gul (1996). 14) In fact, any such game is dominance solvable (see Moulin, 1979, Prop.…”

Payoff Information and Self-Confirming Equilibrium

“…16 In particular, if the game is finite and there is a unique backwards induction solution (which is true for generic 15 The same is true if RSCE is strengthened so that strategies are optimal at all information sets, as in the notion of sequentially RSCE defined in section 4. 16 In this case rationalizability at reachable nodes coincides with its strengthening to sequential rationalizability, which requires optimality at all information sets, as defined in section 4.…”

“…In section 5 we claim that optimality at reachable information sets follows from a natural epistemic model that assumes caution and almost common knowledge (in the sense of Monderer and Samet [19]) of rationality. 6 Reny [21,21], Ben Porath [3] and Gul [16], among others, also argue (in varying degrees of specificity) for optimality at reachable nodes.…”

Common knowledge of payoff uncertainty in games

“…Dekel and Fudenberg (1990) presented a formalisation of conditions involving payoff uncertainty, and linked them to the iterated elimination of strictly dominated strategies preceded by one round of elimination of weakly dominated strategies, the Dekel-Fudenberg procedure. Subsequent game theoretic and logical research zoomed in on the solution concept of the Dekel-Fudenberg procedure and provided epistemic characterisations in terms of approximate common knowledge of rationality (Börgers 1994), a lexicographic variant [90] Synthese (2008) 163:79-97 91 thereof called 'common first-order knowledge' (Brandenburger 1992), the weakest perfect τ -theory (Gul 1996), in terms of players believing that opponents make errors with small (and correlated) probability (Herings and Vannetelbosch 2000), and in terms of common knowledge of perfect rationality (Stalnaker 1996).…”