Equilibrium selection

We present an experiment where two players bargain with a third player. They can bargain either separately or form a joint venture to bargain collectively. Our theoretical benchmark solution predicts decentralized bargaining, as only one player has an interest in forming a joint venture. However, we observe a significant amount of collective bargaining. Collective bargaining, when compared with decentralized bargaining,

This chapter introduces a notion of social/ethical norm that integrates its description as a self- sustaining regularity of behavior with the normative meanings of the statements by which a norm is formulated in the moral language. This definition is applied to organizational ethics where the main problem Ð abuse of authority - is identified with the help of a critical reading of the new-institutional economic theory of the firm. Given a game theoretical definition of an institution, it is then shown that only by integrating it with the social contract as shared mode of reasoning the process of convergence to the beliefs system that backs an equilibrium institution may be started. Thus the chapter illustrates the egalitarian social contract as both an impartial justification for organizational constitutions and as an equilibrium selection device. It is shown that equilibrium selection through the social contract solves the problem of legitimization of authority in the organizational...

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. This generalizes the known mean-field ordinary differential equations and provide a powerful tool to investigate the spatial effects in populations evolution. The

A magnesium-based metal organic framework (MOF), also known as Mg-MOF-74, was successfully synthesized, characterized, and evaluated for adsorption equilibria and kinetics of CO2 and CH4. The Mg-MOF-74 crystals were characterized with scanning electron microscopy for crystal structure, powder X-ray diffraction for phase structure, and nitrogen adsorption for pore textural properties. Adsorption equilibrium and kinetics of CO2 and CH4 on the Mg-MOF-74 adsorbent were measured in a volumetric adsorption unit at 278, 298, and 318 K and pressures up to 1 bar. It was found that the Mg-MOF-74 adsorbent prepared in this work has a median pore width of 10.2 Å, a BET specific surface area of 1174 m2/g, CO2 and CH4 adsorption capacities of 8.61 mmol g−1 (37.8 wt.%) and 1.05 mmol g−1 (1.7 wt.%), respectively, at 298 K and 1 bar. Both CO2 and CH4 adsorption capacities are significantly higher than those of zeolite 13X under similar conditions. The pressure-dependent equilibrium selectivity of CO2 over CH4 (qCO2/qCH4) in the Mg-MOF-74 adsorbent showed a trend similar to that of zeolite 13X and the intrinsic selectivity of Mg-MOF-74 at zero adsorption loading is 283 at 298 K. The initial heats of adsorption of CO2 and CH4 on the Mg-MOF-74 adsorbent were found to be 73.0 and 18.5 kJ mol−1, respectively. The adsorption kinetic measurements suggest that the diffusivities of CO2 and CH4 on Mg-MOF-74 were comparable to those on zeolite 13X. CH4 showed relatively faster adsorption kinetics than CO2 in both adsorbents. The diffusion time constants of CO2 and CH4 in the Mg-MOF-74 adsorbent at 298 K were estimated to be 8.11 × 10−3 and 4.05 × 10−2 s−1, respectively, showing a modest kinetic selectivity of about 5 for the separation CH4 from CO2.Pore size distribution of Mg-MOF-74.► CO2 and CH4 adsorption on Mg-MOF-74 and zeolite 13X. ► CO2/CH4 separation selectivity of 283 on Mg-MOF-74. ► 37.8 wt.% CO2 capacity on Mg-MOF-74 at 298K and 1 bar.

This paper studies the estimation of discrete games of incomplete information when the data may come from multiple equilibria. Most recent work has advocated two-step estimation methods which rely on the assumption that, even if the model has multiple equilibria, a single equilibrium is played in the data. We relax this assumption and study the identification and estimation of this class of models when we impose very weak conditions on the equilibrium selection mechanism. First, we discuss identifica- tion of structural parameters and the equilibrium selection mechanism under different conditions. Second, we propose an algorithm for the estimation of this class of models. An important issue associated the estimation of models with multiple equilibria is that one should maximize the likelihood not only with respect to the structural parame- ters but also with respect to the equilibrium types that generate the observations in the data. If no structure is imposed on equilibrium selecti...

We study cooperation in economies of indefinite duration. Participants faced a sequence of prisonerʼs dilemmas with anonymous opponents. We identify and characterize the strategies employed at the individual level. We report that (i) grim trigger does not describe well individual play and there is wide heterogeneity in strategies; (ii) systematic defection does not crowd-out systematic cooperation; (iii) coordination on cooperative strategies does not improve with experience. We discuss alternative methodologies and implications for theory.► Studies individual strategies in an indefinitely-repeated prisonerʼs dilemma. ► Subjects did not rely on social norms of decentralized punishment. ► Less than one in four subjects adopted the grim trigger strategy. ► Most subjects adopted strategies that do not condition on opponentsʼ actions. ► Systematic defection did not crowd-out systematic cooperation.

Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked. The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players.

We apply three axioms adapted from decision theory to refinements of the Nash equilibria of games with perfect recall that select connected closed sub- sets called solutions. No player uses a weakly dominated strategy in an equilibrium in a solution. Each solution contains a quasi-perfect equilibrium and thus a sequential equilibrium in strategies that provide conditionally admissible optimal continuations from

In economics, the standard approach to language as cheap talk overlooks the fact that natural language is a shared social convention. If a common language is not used, speakers will not be able to understand each other, and truthfulness and belief cannot be defined. In coordination games, we show that a common language can help to select an equilibrium when

Some behavioral economists argue that the honoring of social norms can be adequately modeled as the optimization of social utility functions in which the welfare of others appears as an explicit argument. This paper suggests that the large experimental claims made for social utility functions are premature at best, and that social norms are better studied as equilibrium selection devices

A refinement of the set of Nash equilibria that satisfies two assumptions is shown to select a subset that is stable in the sense defined by Kohlberg and Mertens. One assumption requires that a selected set is invariant to adjoining redundant strategies and the other is a strong version of backward induction. Backward induction is interpreted as the requirement that

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 ...

An interesting problem which has been widely investigated is under what circumstances will a society of rational agents realize some particular stable situations, and whether they satisfy the condition of social efficiency? This will crucially depend on how they interact and what information they have when they interact. For instance, when strategic interactions are modeled as coordination games, it is known the evolutionary process selects the risk-dominant equilibrium which is not necessarily efficient. We consider the networks of agents, in which each agent faces several types of the strategic decision problems. We investigate the dynamics of collective decision when each agent adapts the strategy of interaction to its neighbors. We are interested in to show how the society gropes its way towards an equilibrium situation. We show that the society selects the most efficient equilibrium among multiple equilibria when the agents composing it do learn from each other as collective le...

This paper proposes a method for implementing counterfactual experiments in es-timated models that have multiple equilibria. The method assumes that the researcher does not know the equilibrium selection mechanism and wants to impose minimum restrictions on it. Our key assumption is that the equilibrium selection function does not jump discontinuously between equilibria as we change marginally the structural parameters of the model. Under this assumption, we show that, although the equi-librium selection function is unknown, the researcher can obtain an approximation of this function in a neighborhood of the estimated values of the structural parameters. Under the additional assumption that the counterfactual equilibrium is stable, this ap-proximation can be combined with iterations in the equilibrium mapping to obtain the exact counterfactual equilibrium. We illustrate the differences between our approach and other methods, such as the selection of a counterfactual equilibrium that...

We study experimentally a two-stage compensation mechanism for promoting cooperation in prisoner’s dilemma games. In stage 1, players simultaneously choose binding non-negative amounts to pay their counterparts for cooperating in a given prisoner’s dilemma game, and then play the prisoner’s dilemma game in stage 2 with knowledge of these amounts. For the asymmetric prisoner’s dilemma games we consider, all payment