Deterministic Approximation of Stochastic Evolution in Games

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The processes are Markov chains, and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the discrete stochastic process, for large populations, and its deterministic flow approximation. In particular, we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow. We sharpen these results in the special case of ergodic processes. Copyright Econometric Society, 2002.

Kinship, Incentives, and Evolution

We analyze how family ties affect incentives, with focus on the strategic interaction between two mutually altruistic siblings. The siblings exert effort to produce output under uncertainty, and they may transfer output to each other. With equally altruistic siblings, their equilibrium effort is nonmonotonic in the common degree of altruism, and it depends on the harshness of the environment. We define a notion of local evolutionary stability of degrees of sibling altruism and show that this degree is lower than the kinship-relatedness factor. Numerical simulations show how family ties vary with the environment, and how this affects economic outcomes. (JEL D13, D64, J12, Z13)

Using Markets to Measure Pre-War Threat Assessments: The Nordic Countries facing World War II

Nordic historians have asserted for a long time that in the Nordic countries only few people, if any, perceived increased threats of war prior to the World War II outbreak. This would explain, and possibly excuse, why their governments did not mobilize their armies until it was too late. This paper questions this established notion by deriving new estimates of widely held war threat assessments from the fluctuations of sovereign market yields collected from all Nordic bond markets at this period. Our results show that the Nordic contemporaries indeed perceived significant war risk increases around the time of major war-related geopolitical events. While these findings hence question some, but not all, of the standard Nordic World War II historiography, they also demonstrate the value of analyzing historical market prices to reassess the often tacit views and opinions of large groups of people in the past