People reason about uncertainty with deliberately incomplete models. How do people hampered by different, incomplete views of the world learn from each other? We introduce a model of “ model-based inference.” Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. Unless the differences in agents’ models are trivial, interactions will often not lead agents to have common beliefs or beliefs near the correct-model belief. If the agents’ models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit some bizarre idiosyncrasies and their information is widely dispersed. (JEL D82, D83)

We examine the evolutionary foundations of intertemporal preferences. When all the risk affecting survival and reproduction is idiosyncratic, evolution selects for agents who maximize the discounted sum of expected utility, discounting at the sum of the population growth rate and the mortality rate. Aggregate uncertainty concerning survival rates leads to discount rates that exceed the sum of population growth rate and death rate, and can push agents away from exponential discounting. (JEL D11, D81, D91)

Where do preferences come from? What determines their properties? Though traditionally reluctant to ask such questions, economists have recently turned to evolutionary models for answers. We focus on intertemporal preferences here, arising out of the evolutionary implications of different reproductive strategies or life histories. An agent’s life history specifies the agent’s number and timing (and in a richer model, quality) of offspring. Evolution will select the life history that maximizes the growth rate of the associated group of individuals. We begin with the simplest possible biological life history, that of a semelparous agent that, if it survives a fixed number of years, reproduces and then dies. We show the evolutionary criterion for success in this case entails hyperbolic time discounting of the log of the number of offspring produced. The rate of time preference is a function of age, however, not of time relative to the present, and there are no preference reversals in the sense of behavioral economics. At the same time, the optimal strategy maximizes the exponentially discounted number of offspring, provided we discount at the sum of the death rate and the maximal growth rate. Conventional discounting thus suffices to induce optimal choices from the agent. More generally, if the animal is iteroparous, that is, has a nondegenerate profile of offspring, we show the evolutionary indifference curves over offspring of various ages are hyperplanes that are not parallel, but tilt to reflect greater impatience as the growth rate increases. There is no additively separable function of the age profile of expected offspring that is globally equivalent to this basic biological growth-rate The Evolution of Intertemporal Preferences

This paper examines the patterns of postentry employment growth and failure for over 200,000 plants that entered the U. S. manufacturing sector in the 1967–1977 period. The postentry patterns of growth and failure vary significantly with observable employer characteristics. Plant failure rates decline with size and age as do the growth rates of nonfailing plants. The expected growth rate of a plant, which depends on the net effect of these two forces, declines with size for plants owned by single-plant firms but increases with size for plants owned by multiplant firms.

Abstract: This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify the same behavior on the equilibrium path, but different out-of-equilibrium behavior, appear in connected components of stationary states. The stability properties of these components often depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A sufficient condition is provided for drift to create stationary states with strong stability properties near a component of equilibria. This result is used to derive comparative static predictions concerning common questions raised in the literature on refinements of Nash equlibrium.;

This paper examines an infinite horizon bargaining model, incorporating five features: two-sided incomplete information (with potentially information-revealing strategies), an infinite horizon, uncertainly concerning the potential gains from trade, an illumination of interesting qualitative bargaining issues, and plausible (free from arbitrarily specified out-of-equilibrium conjectures) equilibria. These features, motivated in the paper, have powerful implications. A Nash equilibrium exists, and is generically both unique and sequential. Comparative static implications of variations in the game's specifications are developed. We find that natural indications of bargaining strength emerge from the model, and establish the intuitive result that an increase in a player's relative bargaining strength makes that player more likely to capture the gains from bargaining.

This paper reports an experiment comparing three stag hunt games that have the same best-response correspondence and the same expected payoff from the mixed equilibrium, but differ in the incentive to play a best response rather than an inferior response.In each game, risk dominance conflicts with payoff dominance and selects an inefficient pure strategy equilibrium.We find statistically and economically significant evidence that the differences in the incentive to optimize help explain observed behavior.

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.

We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk-investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations.

We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for noncredible behavior in the presence of imperfect monitoring.