A conventional contract is a contract that each side of a bargain expects the other side to insist on, because it is standard and customary under the circumstances. The author considers a process of convention formation in which agents expectations evolve through repeated interactions in a large-population setting. Agents choose best replies given their knowledge of the precedents, subject to some inertia and random error in their choice behavior. Over the long run, this adaptive learning process tends to select contracts that are efficient, and egalitarian in the sense that the payoffs are centrally located on the efficiency frontier of the payoff possibility set. When the payoffs form a convex, comprehensive bargaining set, the process selects the Kalai-Smorodinsky solution.

Survey data suggest that cropsharing contracts exhibit a much higher degree of uniformity than is warranted by economic fundamentals. We propose a dynamic model of contract choice to explain this phenomenon. Landowners and tenants recontract periodically, taking into account expected returns as well as conformity with local practice. The resulting stochastic dynamical system is studied using techniques from statistical mechanics. The most likely states consist of patches where contractual terms are nearly uniform, separated by boundaries where the terms shift abruptly. These and other predictions of the model are borne out by survey data on agricultural contracts in Illinois.

The author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality. The game is repeated many times by different players. Each player chooses an optimal reply based on incomplete information about what other players have done in the past. Occasionally they make mistakes. When the likelihood of mistakes is very small, typically one coordination equilibrium will be played almost all of the time over the long run. This stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed Markov processes.

New ideas, products, and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. This paper examines three broad classes of diffusion models—contagion, social influence, and social learning—and shows how to incorporate heterogeneity into each at a high level of generality without losing analytical tractability. Each type of model leaves a characteristic “footprint” on the shape of the adoption curve which provides a basis for discriminating empirically between them. The approach is illustrated using the classic study of Ryan and Gross (1943) on the diffusion of hybrid corn.

The recent financial crisis has prompted much new research on the interconnectedness of the modern financial system and the extent to which it contributes to systemic fragility. Network connections diversify firms' risk exposures, but they also create channels through which shocks can spread by contagion. We review the extensive literature on this issue, with the focus on how network structure interacts with other key variables such as leverage, size, common exposures, and short-term funding. We discuss various metrics that have been proposed for evaluating the susceptibility of the system to contagion and suggest directions for future research.

Interconnections among financial institutions create potential channels for contagion and amplification of shocks to the financial system. We estimate the extent to which interconnections increase expected losses and defaults under a wide range of shock distributions. In contrast to most work on financial networks, we assume only minimal information about network structure and rely instead on information about the individual institutions that are the nodes of the network. The key node-level quantities are asset size, leverage, and a financial connectivity measure given by the fraction of a financial institution’s liabilities held by other financial institutions. We combine these measures to derive explicit bounds on the potential magnitude of network effects on contagion and loss amplification. Spillover effects are most significant when node sizes are heterogeneous and the originating node is highly leveraged and has high financial connectivity. Our results also highlight the importance of mechanisms that go beyond simple spillover effects to magnify shocks; these include bankruptcy costs, and mark-to-market losses resulting from credit quality deterioration or a loss of confidence. We illustrate the results with data on the European banking system.

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here, we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young (2014) demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs.