Two more classes of games with the continuous-time fictitious play property

Fictitious Play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for several classes of games, including weighted potential games, supermodular games with diminishing returns, and 3×3 supermodular games. Extending these results, we establish convergence of Continuous-time Fictitious Play for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3×m and 4×4 quasi-supermodular games.     

Joint Production and the Structure of Technology: A Generalization

In this paper, we have a peek inside the black box of technology in an attempt to get a better understanding of the concept of joint production. We introduce the notion of input and output subtechnologies; these are then used as building blocks to define various types of production processes, either joint or nonjoint. Thus, in the 2×2 case, we are able to identify up to 36 different production structures, some of which are well known, but most of which are new. These are all described in the primal quantity space as well as in the dual price space. Comparative statics results for the 2×2 joint production process are derived.     

Capacity Choices and Price Competition in Experimental Markets

We report on experimental duopoly markets with heterogeneous goods. In these markets, sellers first choose capacities and then prices. While capacities remain fixed for either five or ten periods, prices have to be chosen in every period. The experiments starts with two sets of exogenously predetermined capacities. Independently of the distribution of capacities is, a unique pure-strategy in prices is subgame perfect. In equilibrium, capacities should correspond to the Cournot prediction. Given capacities, price-setting behavior is in general consistent with the theory. Average capacities converge above the Cournot level. Capacities converge at the industry level but are somewhat dispersed. Sellers rarely manage to cooperate.     

A discrete model of optimal economic growth

Contrary to most of the literature on optimal economic growth a discrete rather than a continuous model is investigated. It is shown that in such a discrete model it is easy to account for relatively freely changing functions and parameters. Thus, the production function, labor, the investment ratio, and the parameters for time preference, marginal utility, and depreciation are all allowed to depend on time. Using discrete dynamic programming methods, optimal investment policies are determined explicitly. These generalize important results from previous literature on optimal economic growth.     

Learning in games with strategic complementarities revisited

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.