On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)      

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

Scale functions in equilibrium selection games

We present here an evolutionary game model, and address the issue of equilibrium selection working with the scale function of a diffusion process describing the dynamics of population processes with mutation modeled as white noise. This model is the same as the one in Foster and Young (1990) but with a different interpretation at the boundaries and with different mutation modelings. First, we justifiably assume that the boundaries of the solution of the stochastic differential equation are absorbing so that the first boundary of the interval [0,1] hit will determine the equilibrium selected. Then, working with the scale function, we obtain for 2×2 symmetric games and different mutation parameters, some new and interesting equilibrium selection results. The aim of this article is to describe another method of approach in evolutionary games with mutation which we believe will prove to be very useful in studying more general normal form games and different mutation modelings.     

On the motivations for the dual-use of electronic and traditional cigarettes

We apply a classical economic categorization of preferences to identify the motivations of dual-users of electronic and traditional cigarettes. The responses of 2406 US adults (including 413 dual-users) in 2015 were collected using a novel online survey along with a follow-up in 2016 of 143 of these adults (68 dual-users). A sizeable minority of 37% of dual-users reported viewing electronic and conventional cigarettes primarily as complements. Of those who had never smoked or used electronic cigarettes, only 27% thought the complementarity motive would be primary. Dual-user motivations were associated with quit-attempt, cessation methods, gender and age. 1 year on, there was a positive relationship between the level of complementarity in the dual-user’s motives and their change in self-reported traditional cigarette consumption. It is concluded that the application of a canonical economic classification of preferences may reveal important heterogeneities among the dual-user population.     

Equilibrium selection in coordination games with simultaneous play

Summary. We apply the dynamic stochastic framework proposed in recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games payoffs, and hence best replies, are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be made stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Received: February 12, 2001; revised version: October 29, 2001     

Games played in a contracting environment

We analyze normal form games where a player has to pay a price to a supplier in order to play a specific action. Our focus is on supplier competition, arising from the fact that distinct suppliers supply different players, and possibly different actions of the same player. With private contracts, where a player only observes the prices quoted by his own suppliers, the set of equilibrium distributions over player actions coincides with the set of equilibrium distributions when all actions are supplied competitively, at cost. With public contracts, the two distributions differ dramatically even in simple games.     

Evidence on learning in coordination games

This paper reports an experiment designed to detect the influence of strategic uncertainty on behavior in order statistic coordination games, which arise when a player’s best response is an order statistic of the cohort’s action combination. Unlike previous experiments using order statistic coordination games, the new experiment holds the payoff function constant and only changes cohort size and order statistic.

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Shadows of the past: path dependence of TV on its sub-systems,complements and substitutes

In this study, two levels of path dependence in the television technological system are examined: (1) How does the development of television (TV) core components affect the development of peripheral components? and (2) How does the development of complementary and substitute technologies affect the development of television technology? Results from the empirical analysis using patents from 1975 to 2004 indicate that: (a) the development of TV periphery technologies is path-dependent on the development of TV core technologies and (b) even after controlling for its own prior history, the development of the TV system is path-dependent on the development of its complementary technologies. However, there is weak evidence of the path dependence of the TV system on the development of its substitute technologies.