Prices and quality signals

We consider a market-for-lemons model where the seller is a price setter, and, in addition to observing the price, the buyer receives a private noisy signal of the product's quality, such as when a prospective buyer looks at a car or house for sale, or when an employer interviews a job candidate. Sufficient conditions are given for the existence of perfect Bayesian equilibria, and we analyze equilibrium prices, trading probabilities and gains of trade. In particular, we identify separating equilibria with partial and full adverse selection as well as pooling equilibria. We also study the role of the buyer's signal precision, from being completely uninformative (as in standard adverse-selection models) to being completely informative (as under symmetric information). The robustness of results for these two boundary cases is analyzed, and comparisons are made with established models of monopoly and perfect competition.lemons; noisy quality signal; adverse selection

Language, meaning and games: a model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of two-sided pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to finite and symmetric two-player games and we establish that, in generic and symmetric n x n -coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We discus Aumann’s (1990) example of a Pareto efficient equilibrium that is not self-enforcing. We also extend the approach to one-sided communication.Communication, coordination, language, honesty, evolutionary stability.

Outer measure and utility

In most economics textbooks there is a gap between the non-existence of utility functions and the existence of continuous utility functions, although upper semi-continuity is sufficient for many purposes. Starting from a simple constructive approach for countable domains and combining this with basic measure theory, we obtain necessary and sufficient conditions for the existence of upper semi-continuous utility functions on a wide class of domains. Although links between utility theory and measure theory have been pointed out before, to the best of our knowledge this is the first time that the present route has been taken.preferences; utility theory; measure theory; outer measure

Uniqueness in Infinitely Repeated Decision Problems

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We provide a sufficient condition for uniqueness in a class of such games, namely infinitely repeated decision problems with discounting. The condition is two-fold: the range of possible utility levels in the decision problem should be bounded from below, and the discount factor between successive periods should be non-decreasing over time, a condition met by exponential, quasi-exponential and hyperbolic discounting.  Game Theory; Time Preference; Hyperbolic Discounting; Repeated Decision Problems

Punctuality - A Cultural Trait as Equilibrium

A people's culture, norms and habits are important determinants not just of the quality of social life but of economic progress and growth. In this paper we take the view that while the importance of culture is undeniable, the innateness of culture is not. We work here with a single example and demonstrate how a human trait which is widely believed to be cultural is at the same time a matter of choice. The example that we shall work with concerns punctuality. We show that punctuality may be simply an equilibrium response of individuals to what they expect others to do. The same society can get caught in a punctual equilibrium or a non-punctual equilibrium. Punctuality; Coordination Games

Price competition and convex costs

In the original model of pure price competition, due to Joseph Bertrand (1883), firms have linear cost functions. For any number of identical such price-setting firms, this results in the perfectly competitive outcome; the equilibrium price equal the firms' (constant) marginal cost. This paper provides a generalization of Bertrand's model from linear to convex cost functions. I analyze pure price competition both in a static setting - where the firms interact once and for all - and in dynamic setting - where they interact repeatedly over an indefinite future. Sufficient conditions are given for the existence of Nash equilibrium in the static setting and for subgame perfect equilibrium in the dynamic setting. These equilibrium sets are characterized, and it is shown that there typically exists a whole interval of Nash equilibrium prices in the static setting and subgame perfect equilibria in the dynamic setting. It is shown that firms may earn sizable profits and that their equilibrium profits may increase if their production costs go up

Deterministic Approximation of Stochastic Evolution in Games

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the stochastic process, for large populations, and its deterministic approximation. In particular, we show that if the deterministic solution through the initial state of the stochastic process at some point in time enters a basin of attraction, then the stochastic process will enter any given neighborhood of that attractor within a finite and deterministic time with a probability that exponentially approaches one as the population size goes to infinity. The process will remain in this neighborhood for a random time that almost surely exceeds an exponential function of the population size. During this time interval, the process spends almost all time at a certain subset of the attractor, its so-called Birkhoff center. We sharpen this result in the special case of ergodic processes.  Game Theory; Evolution; Approximation

What have we learned from Evolutionary Game Theory so far?

Evolutionary theorizing has a long tradition in economics. Only recently has this approach been brought into the framework of non-cooperative game theory. Evolutionary game theory studies the robustness of strategic behaviour with respect to evolutionary forces in the context of games played many times in large populations of boundedly rational agents. This new strand in economic theory has lead to new predictions and opened up doors to other social sciences. The discussion will be focused on the following questions: What distinguishes the evolutionary approach from the rationalistic? What are the most important findings in evolutionary game theory so far? What are the next challenges for evolutionary game theory in economics

Managerial Incentives and Market Integration

This paper develops a new analytical approach to the old question whether market conditions may influence the internal efficiency of firms. The basic textbook model of the firm is slightly extended to incorporate managers' incentives to reduce production costs in an imperfectly competitive product market. This is done without invoking any agency problem or other form of information asymmetry in firms. The analysis extends Marshallian and Hicksian consumer analysis to managers' demand for leisure in imperfectly competitive environments with a fixed number of firms, and free entry, respectively. Conditions are identified under which product market integration enhances the internal efficiency of firms, and it is shown that market integration is Pareto improving under free entry

Internal Efficiency and External Conditions

This paper develops a new analytical approach to the old question whether market conditions may influence the internal efficiency of firms. The basic textbook model of the firm is slightly extended to incorporate managers' incentives to reduce production costs in an imperfectly competitive product market. This is done without invoking any agency problem or other form of information asymmetry. The analysis extends Marshallian and Hicksian consumer analysis to managers' demand for leisure in imperfectly competitive environments with a fixed number of firms, and free entry, respectively. Conditions are identified under which product market integration enhances the internal efficiency of firms, and it is shown that market integration is Pareto improving under free entry