Dominance-Solvable Lattice Games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs.

Maximum Sustainable Government Debt in the Overlapping Generations Model.

The theoretical determinants of maximum sustainable government debt are investigated using Diamond's overlapping-generations model. A level of debt is defined to be 'sustainable' f a steady state with non-degenerate values of economic variables exists. We show that a maximum sustainable level of debt almost always exists. Most interestingly, it normally occurs at a 'catastrophe' ather than a 'degeneracy' , i.e. where variables such as capital and consumption are in the interiors, rather than at the limits, of their economically meaningful ranges. This means that if debt is increased step by step, the economy may suddenly collapse without obvious warning.GOVERNMENT DEBT ; OVERLAPPING GENERATIONS

Dominance-solvable lattice games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs

When are plurality rule voting games dominance-solvable?

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of plurality rule voting games. For K > 3 alternatives and n > 3 voters, we find sufficient conditions for the game to be dominance-solvable (DS) and not to be DS. These conditions can be stated in terms of only one statistic of the game, the largest proportion of voters who agree on which alternative is worst in a sequence of subsets of the original set of alternatives. When n is large, “almost all” games can be classified as either DS or not DS. If the game is DS, a Condorcet Winner always exists when n > 4, and the outcome is always the Condorcet Winner when the electorate is sufficiently replicate

Global games and equilibrium selection

Game Theory;Equilibrium Theory

Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.Dynamic Programming; Bellman Equation; Unbounded Returns

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.