On extended liability in a model of adverse selection

We consider a model where a judgment-proof firm needs finance to realize a project. This project might cause an environmental hazard with a probability that is the private knowledge of the firm. Thus there is asymmetric information with respect to the environmental riskiness of the project. We consider the implications of a simple joint and strict liability rule on the lender and the firm where, in case of a damage, the lender is responsible for that part of the liability which the judgment-proof firm cannot pay. We use a weighted version of the neutral bargaining solution (Myerson 1983 / 1984) to determine the financial contract between the lender and the firm. In the given model we show that either full or a punitive liability is optimal.judgement proofness, extended liability, neutral bargaining solution.

An Experiment on Forward versus Backward Induction: How Fairness and Levels of Reasoning Matter

We report the experimental results on a game with an outside option where induction contradicts with background induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selton's (1888) theory, which is hence here in contradiction with strategic stability (Kohlberg-Mertens (1985)). We find the Harsanyi-Selton solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Fehr and Schmidt (1999), Bolton and Ockenfels (2000), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of "fairness equilibra", some of which seem to be rejected because they require too many levels of reasoning"experiments, equilibrium selection, forward induction, fairness, levels of reasoning.

Where strategic and evolutionary stability depart - a study of minimal diversity games

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.Strategic form games, strategic stability, evolutionary stability

Using Economic Classroom Experiments

Economic classroom experiments are an excellent way to increase student interest, but getting started may be difficult. We attempt to aid the newcomer by recommending which experiments to use and describing the current resources available.

On the Evolutionary Selection of Nash Equilibrium Components

It is well known for the common multi-population evolutionary dynamics applied to normal form games that a pure strategy combination is asymptotically stable if and only if it is a strict equilibrium point. We extend this result to sets as follows. For certain regular selection dynamics every connected and closed asymptotically stable set of rest points containing a pure strategy combination is a strict equilibrium set and hence a Nash equilibrium component. A converse statement holds for two person games, for convex strict equilibrium sets and for the standard replicator dynamic.evolutionary dynamics, replicator dynamic, regular selection dynamics, strict equilibrium set, Nash equilibrium component.

Refined best reply correspondence and dynamics

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has (1) a product structure, is (2) upper semi-continuous, (3) always includes a best reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each generalized best reply correspondence we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set-inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We ultimately find that every Kalai and Samet's (1984) persistent retract, which coincide with Basu and Weibull's (1991) CURB sets based, however, on the refined best reply correspondence, contains a MASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again, however, based on the refined best reply correspondence.Evolutionary game theory, best response dynamics, CURB sets, persistent retracts, asymptotic stability, Nash equilibrium refinements, learning

Neutral optima in informed principal problems with common values

Working paperIn a class of informed principal problems with common values often used in applications we define a particular mechanism which we call the assured allocation. It is always undominated, i.e. efficient among the different types of the principal. We show it is a perfect Bayesian equilibrium allocation of the three-stage game studied in Maskin and Tirole (1992) that coincides with the Rothschild-Stiglitz-Wilson allocation when the latter is undominated. Under familiar conditions on hazard rates we show that the assured allocation is a neutral optimum in the sense of Myerson (1983)

Refined best-response correspondence and dynamics

We characterize the smallest faces of the polyhedron of strategy profiles that could possibly be made asymptotically stable under some reasonable deterministic dynamics. These faces are Kalai and Samet's (1984) persistent retracts and are spanned by Basu and Weibull's (1991) CURB sets based on a natural (and, in a well-defined sense, minimal) refinement of the best-reply correspondence. We show that such a correspondence satisfying basic properties such as existence, upper hemi-continuity, and convex-valuedness exists and is unique in most games. We introduce a notion of rationalizability based on this correspondence and its relation to other such concepts. We study its fixed-points and their relations to equilibrium refinements. We find, for instance, that a fixed point of the refined best reply correspondence in the agent normal form of any extensive form game constitutes a perfect Bayesian equilibrium, which is weak perfect Bayesian in every subgame. Finally, we study the index of its fixed point components.Evolutionary game theory, best response dynamics, CURB sets, persistent retracts, asymptotic stability, Nash equilibrium refinements, learning

Teaching Bank Runs with Classroom Experiments

Once relegated to cinema or history lectures, bank runs have become a modern phenomenon that captures the interest of students. We use a simple classroom experiment based upon the Diamond-Dybvig Model (1983) to demonstrate how a bank run, a seemingly irrational event, can occur rationally. We then present possible topics for discussion including various ways to prevent bank runs and moral hazard.bank runs; multiple equilibria