Economic Darwinism

We define an evolutionary process of “economic Darwinism” for playing the field, symmetric games. The process captures two forces. One is “economic selection”: if current behavior leads to payoff differences, behavior yielding lowest payoff has strictly positive probability of being replaced by an arbitrary behavior. The other is “mutation”: any behavior has at any point in time a strictly positive, very small probability of shifting to an arbitrary behavior. We show that behavior observed frequently is in accordance with “evolutionary equilibrium”, a static equilibrium concept suggested in the literature. Using this result, we demonstrate that generally under positive (negative) externalities, economic Darwinism implies even more under- (over-)activity than does Nash equilibrium.     

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.     

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.We are grateful to Birgit Grodal, Salvatore Modica, David Schmeidler, and an anonymous referee for comments, help, and encouragement. Financial support from the Danish Social Sciences Research Council is acknowledged.     

Testing the Intransitivity Explanation of the Allais Paradox

This paper uses a two-dimensional version of a standard common consequence experiment to test the intransitivity explanation of Allais-paradox-type violations of expected utility theory. We compare the common consequence effect of two choice problems differing only with respect to whether alternatives are statistically correlated or independent. We framed the experiment so that intransitive preferences could explain violating behavior when alternatives are independent, but not when they are correlated. We found the same pattern of violation in the two cases. This is evidence against intransitivity as an explanation of the Allais Paradox. The question whether violations of expected utility are mainly due to intransitivity or to violation of independence is important since it is exactly on this issue the main new decision theories differ.