Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

The marginal utility of money: A modern Marshallian approach to consumer choice

We reformulate neoclassical consumer choice by focusing on lambda, the marginal utility of money. As the opportunity cost of current expenditure, lambda is approximated by the slope of the indirect utility function of the continuation. We argue that lambda can largely supplant the role of an arbitrary budget constraint in partial equilibrium analysis. The result is a better grounded, more flexible and more intuitive approach to consumer choice.

Tractable Consumer Choice

We derive a rational model of separable consumer choice which can also serve as a behavioral model. The central construct is [lambda] , the marginal utility of money, derived from the consumer's rest-of-life problem. We present a robust approximation of [lambda], and show how to incorporate liquidity constraints, indivisibilities and adaptation to a changing environment. We fi nd connections with numerous historical and recent constructs, both behavioral and neoclassical, and draw contrasts with standard partial equilibrium analysis. The result is a better grounded, more flexible and more intuitive description of consumer choice.