Paulo Barelli

A note on the equilibrium existence problem in discontinuous games

In this note, we prove an equilibrium existence theorem for games with discontinuous payoffs and convex and compact strategy spaces. It generalizes the classical result of Reny (1999), as well as the recent paper of McLennan, Monteiro, and Tourky (2011). Our conditions are simple and easy to verify. Importantly, examples of spatial location models show that our conditions allow for economically meaningful payoff discontinuities, that are not covered by other conditions in the literature.

On the genericity of full surplus extraction in mechanism design

Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233], using convex combinations of models, showed that full surplus extraction (FSE) in mechanism design is generically impossible, contrary to the seminal work of Cremer and McLean [J. Cremer, R. McLean, Full extraction of the surplus in Bayesian and dominant strategy auctions, Econometrica 53 (1988) 345-361]. Since Cremer and McLean did not allow convex combinations of models, the two results are not comparable. We show that FSE is generically impossible when convex combinations of models are not allowed, provided that we do not hold fixed the cardinality of models.

Rent‐Seeking and Capital Accumulation

A general model incorporating rent‐seeking activities in the standard neoclassical model of capital accumulation is presented. The welfare of the representative agent is negatively affected by the efficiency of rent‐seeking activities. Although intuitive, this result is not obvious because long‐run income can be positively affected by more efficient rent‐seeking activities. The model is used to provide explanations for some recent experiences in developing countries, including the relative poor performance of economies that experience a move to a more decentralized system and the observed path of total factor productivity (TFP) in countries like Ireland and Venezuela.

A note on semi-Markov perfect equilibria in discounted stochastic games

We establish that general discounted stochastic games with state transitions that are absolutely continuous with respect to a fixed, atomless measure admit stationary semi-Markov perfect equilibria, i.e., equilibria in which each players action depends only on the current state and on the previous state and action profile. This resolves an open existence question stemming from an error in the proof of Theorem 4 of Chakrabarti [3]. Moreover, the result follows from “un-correlating” Nowak and Raghavans [25] stationary correlated equilibrium, establishing that there is no need to resort to additional, unmodeled state variables.

Admissibility and Event-Rationality

We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other playersʼ strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that event-rationality and common belief of event-rationality (RCBER) imply S∞W, the set of admissible strategies that survive iterated elimination of dominated strategies. By strengthening standard belief to validated belief, we show that event-rationality and common validated belief of event-rationality (RCvBER) imply IA, the iterated admissible strategies. We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, hence providing epistemic criteria for S∞W and IA.

A Model of Capital Accumulation and Rent-Seeking

A simple model incorporating rent-seeking into the standard neoclassical model of capital accumulation is presented. It embodies the idea that the performance of an economy depends on the efficiency of its institutions. It is shown that welfare is positively affected by the institutional efficiency, although output is not necessarily so. It is also shown that an economy with a monopolistic rent-seeker performs better than one with a competitive rent-seeking industry.

Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions

We prove existence and purification results for strategic environments possessing a product structure that includes classes of large games, stochastic games, and models of endogenous institutions. Applied to large games, the results yield existence of pure-strategy equilibria allowing for infinite-dimensional externalities. Applied to stochastic games, the results yield existence of stationary Markov perfect equilibria with extremal payoffs, which in turn yields existence of pure strategy stationary Markov perfect equilibria for games with sequential moves. Applied to the model of institutions, we obtain equilibrium existence with general group decision correspondences.

Purification of Bayes Nash equilibrium with correlated types and interdependent payoffs

We establish purification results for Bayes–Nash equilibrium in a large class of Bayesian games with finite sets of pure actions. We allow for correlated types and interdependent payoffs and for type-dependent feasible action sets. The latter feature allows us to prove existence and purification results for pure Bayes–Nash equilibria in undominated strategies. We give applications to auctions, global games, and voting to illustrate the usefulness of our results.