Equilibrium Selection in Static and Dynamic Entry Games

We experimentally examine equilibrium refinements in static and dynamic binary choice games of complete information with strategic complementarities known as “entry†games. Our aim is to assess the predictive power of two different equilibrium selection principles. In static entry games, we test the theory of global games as an equilibrium selection device. This theory posits that players play games of complete information as if they were playing a related global game of incomplete information. In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs it is irreversible. The number of people who have already entered is part of the state description, and individuals can condition their decisions on that information. If the state variable does not indicate that entry is dominated, the efficient subgame perfect equilibrium prediction calls for all players to enter. Further, if there is a cost of delay, entry should occur immediately, thereby eliminating the coordination problem. This subgame perfect entry threshold in the dynamic game will generally differ from the global game threshold in static versions of the same entry game. Nevertheless, our experimental findings suggest that observed entry thresholds in both static and dynamic versions of the same entry game are surprisingly similar. The mean entry threshold in the static game lies below the global game equilibrium threshold while the mean entry threshold in the dynamic game lies above the efficient subgame perfect equilibrium threshold. An important implication of this finding is that if one were to observe only the value of the state variable and the number of people who enter by the end of the game one could not determine whether the static or the dynamic game had been played.

A Semiparametric Test of Agent's Information Sets for Games of Incomplete Information

We propose semiparametric tests of misspecification of agent's information for games of incomplete information. The tests use the intuition that the opponent's choices should not predict a player's choice conditional on the proposed information available to the player. The tests are designed to check against some commonly used null hypotheses (Bajari et al. (2010), Aradillas-Lopez (2010)). We show that our tests have power to discriminate between common alternatives even in small samples. We apply our tests to data on entry in the US airline industry. Both the assumptions of independent and correlated private shocks are not supported by the data

Recent developments in empirical IO: dynamic demand and dynamic games

Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the "inclusive value" to deal with dimensionality problems and reduce the computational burden. We clarify the assumptions needed for this approach to work, the implications for the treatment of heterogeneity and the different ways it has been used. In our discussion of the econometrics of dynamics games of oligopoly competition, we deal with challenges related to estimation and counterfactual experiments in models with multiple equilibria. We also examine methods for the estimation of models with persistent unobserved heterogeneity in product characteristics, firms’ costs, or local market profitability. Finally, we discuss different approaches to deal with large state spaces in dynamic games.Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity.

Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games

Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the \Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity.

Recovering the sunk costs of R&D: the moulds industry case

Sunk costs for R&D are an important determinant of the level of innovation in the economy. In this paper I recover them using a Markov equilibrium framework. The contribution is twofold. First, a model of industry dynamics which accounts for selection into R&D, capital accumulation and entry/exit is proposed. The industry state is summarized by an aggregate state with the advantage that it avoids the "curse of dimensionality". Second, the estimated sunk costs of R&D for the Portuguese moulds industry are shown to be important (3.4 million Euros). They become particularly relevant since the industry is mostly populated by small firms. Institutional changes in the early 1990s generated an increase in demand from European car makers and created the incentives for firms to pay the costs of investment. Trade-induced innovation reinforced the selection effect by which international trade leads to productivity growth. Finally, using the estimated parameters, simulations evaluate the effects of changes in market size, sunk costs and entry costs

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs

Recovering the Sunk Costs of R&D: the Moulds Industry Case

Sunk costs for R&D are an important determinant of the level of innovation in the economy. In this paper I recover them using a Markov equilibrium framework. The contribution is twofold. First, a model of industry dynamics which accounts for selection into R&D, capital accumulation and entry/exit is proposed. The industry state is summarized by an aggregate state with the advantage that it avoids the "curse of dimensionality". Second, the estimated sunk costs of R&D for the Portuguese moulds industry are shown to be important (3.4 million Euros). They become particularly relevant since the industry is mostly populated by small firms. Institutional changes in the early 1990s generated an increase in demand from European car makers and created the incentives for firms to pay the costs of investment. Trade-induced innovation reinforced the selection effect by which international trade leads to productivity growth. Finally, using the estimated parameters, simulations evaluate the effects of changes in market size, sunk costs and entry costs.Aggregate state, industry dynamics, Markov equilibrium, moulds industry, R&D, structural estimation, sunk costs

Semi-dynamic Hawk and dove game, applied to power control

In this paper, we study a power control game over a collision channel. Each player has an energy state. When choosing a higher transmission power, the chance of a successful transmission (in the presence of other interference) increases at the cost of a larger decrease in the energy state of the battery. We study this dynamic game when restricting to simple non-dynamic strategies that consist of choosing a given power level that is maintained during the lifetime of the battery. We identify a surprising paradox in our Hawk-Dove game which we term the initial energy paradox