Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium

In this article we combine Debreu’s (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 2008) ideas of embedding a “desired” game form into a “natural” game form that includes all feasible behavior, even if it is “illegal” according to the desired form. For the resulting socio-legal system we extend Debreu’s concepts of a social system and its social equilibria to a socio-legal system with its Debreu–Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (J Math Econ 2(3):345–348, 1975) that also generalizes the dc-mechanism of Koray and Yildiz (J Econ Theory 176:479–502, 2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (Designing rights: invisible hand theorems, covering and membership. Tech. rep. Mimeo, Bogazici University, 2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two person cooperative bargaining. There we provide in a socio-legal system based on Nash’s demand game an implementation of the Nash bargaining solution in Debreu–Hurwicz equilibrium.

Bounded rational response equilibria in human sensorimotor interactions

The Nash equilibrium is one of the most central solution concepts to study strategic interactions between multiple players and has recently also been shown to capture sensorimotor interactions between players that are haptically coupled. While previous studies in behavioural economics have shown that systematic deviations from Nash equilibria in economic decision-making can be explained by the more general quantal response equilibria, such deviations have not been reported for the sensorimotor domain. Here we investigate haptically coupled dyads across three different sensorimotor games corresponding to the classic symmetric and asymmetric Prisoner's Dilemma, where the quantal response equilibrium predicts characteristic shifts across the three games, although the Nash equilibrium stays the same. We find that subjects exhibit the predicted deviations from the Nash solution. Furthermore, we show that taking into account subjects' priors for the games, we arrive at a more accurate description of bounded rational response equilibria that can be regarded as a quantal response equilibrium with non-uniform prior. Our results suggest that bounded rational response equilibria provide a general tool to explain sensorimotor interactions that include the Nash equilibrium as a special case in the absence of information processing limitations.

Wage Bargaining and Minimum Wages in a Search–Matching Model

In this paper, we analyze the introduction of a nonbinding minimum wage in a search–matching model with wage bargaining. Applying the Kalai–Smorodinsky bargaining solution instead of the commonly applied Nash solution, we provide a theoretical explanation for spillover effects of minimum wages on other wages higher up in the wage distribution. The labor market equilibrium in the Kalai–Smorodinsky solution with a minimum wage is characterized by lower market tightness, a higher unemployment rate, and lower vacancy rate than the equilibrium in the Nash solution. Moreover, we show that a nonbinding minimum wage can increase social welfare.

An OLG Differential Game of Pollution Control with the Risk of a Catastrophic Climate Change

This paper studies an overlapping generations (OLG) differential game on optimal emissions with continuous age structure and different types of individuals. At the (stochastic) arrival of a catastrophic climate change, the utility and the damage to the stock of pollution change for the rest of the time horizon. We derive the open-loop (OL) Nash equilibrium and show that it is subgame perfect and moreover equal to the feedback Stackelberg one. We compare the solution to the cooperative one (using the social welfare as objective function) and show the different dynamic evolutions of optimal emissions over time. Finally, we derive a time-consistent tax scheme that reaches the cooperative optimal solution in the OL Nash equilibrium. The tax scheme turns out to be heterogeneous with respect to age and type (anticipating and nonanticipating the catastrophic climate change). Setting taxes that are homogeneous across the individual type leads to an OL Nash solution that produces socially optimal total emissions, but lower individual utilities.

Ultimatum Game Bargaining Behaviour: A Classroom Experiment

This study aims to investigate the types of bargaining behaviour students have and the variables that affect these bargaining behaviours by designing an ultimatum bargaining game in the classroom environment (during the real exam). The experimental group consists of 202 students who took the spring term economics final exam. The strategic interaction between students was formulated as a two-person bargaining problem. A cooperative solution was based on the Nash solution also obtained for bargaining problem among students. The findings of this study show that the highest bargaining equilibrium in this game is the equilibrium status based on the Nash solution. Moreover, we concluded that the success of the economy course and the grade-level affect the students’ behaviour according to the equilibrium strategy based on the Nash solution. JEL Codes: C90, C70, C78, C57

The Nash Solution as a von Neumann–Morgenstern Utility Function on Bargaining Games

In this paper we prove that the symmetric Nash solution is a risk neutral von Neumann–Morgenstern utility function on the class of pure bargaining games. Our result corrects an error in Roth (Econometrica 46:587–594, 983, 1978) and generalizes Roth’s result to bargaining games with arbitrary status quo.