Nullified equal loss property and equal division values

We provide characterizations of the equal division values and their convex mixtures, using a new axiom on a fixed player set based on player nullification which requires that if a player becomes null, then any two other players are equally affected. Two economic applications are also introduced concerning bargaining under risk and common-pool resource appropriation.     

Alternating-Offer Bargaining and Common Knowledge of Rationality

This paper reconsiders Rubinstein's alternating-offer bargaining game with complete information. We define rationalizability and trembling- hand rationalizability (THR) for multi-stage games with observed actions. We show that rationalizability does not exclude perpetual disagreement or delay, but that THR implies a unique solution. Moreover, this unique solution is the unique subgame perfect equilibrium (SPE). Also, we reconsider an extension of Rubinstein's game where a smallest money unit is introduced: THR rules out the non-uniqueness of SPE in some particular case. Finally, we investigate the assumption of boundedly rational players. Perpetual disagreement is excluded, but not delay. Furthermore, we cannot use the asymmetric Nash bargaining solution as an approximation of the alternating-offer bargaining model once the players are boundedly rational ones.     

Simultaneous moves multi-person continuous time concession game

The alternating offers strategic bargaining approach (Rubinstein, 1982) suggest a unique perfect equilibrium. In this equilibrium the bargaining ends immediately and the outcome is Pareto optimal. In this paper we consider a bargaining game in which players move simultaneously. Since we allow players only to lower their demands over time we denote this game as a concession game. We demonstrate that in this game there is a perfect equilibrium in which the bargaining lasts long enough so that the pie shrinks to zero. We show that we can generalize this game to a multi-player concession game in a straightforward manner and so avoiding the difficulties of generalizing the alternating offers game to the multi-player case.     

Mechanism robustness in multilateral bargaining

This paper discusses the relationship between coalitional stability and the robustness of bargaining outcomes to the bargaining procedure. We consider a class of bargaining procedures described by extensive form games, where payoff opportunities are given by a characteristic function (cooperative) game. The extensive form games differ on the probability distribution assigned to chance moves which determine the order in which players take actions. One way to define mechanism robustness is in terms of the property of no first mover advantage. An equilibrium is mechanism robust if for each member the expected payoff before and after being called to propose is the same. Alternatively one can define mechanism robustness as a property of equilibrium outcomes. An outcome is said to be mechanism robust if it is supported by some equilibrium in all the extensive form games (mechanisms) within our class. We show that both definitions of mechanism robustness provide an interesting characterization of the core of the underlying cooperative game.     

Pretrial Bargaining in the Face of a Random Court Decision: Evidence from Laboratory Games

If negotiation over ownership of an asset is unsuccessful, agents go to court to determine possession. Experiments examine how the presence of a stochastic court decision affects pretrial bargaining behavior. Two players have private information over the value of an asset, owned by one player. If there is no acceptable trade price, a random court decision assigns ownership. The impact of a second stage court decision on bargaining outcomes and the efficiency of trades is measured. Courts reduce the total earnings of players and the frequency of efficient trades. Relative earnings and bargaining behavior depend on which agent proposes the trade price.     

Spatial bargaining in rectilinear facility location problem

Theory and Decision - We consider a spatial bargaining model where players collectively choose a facility location on a two-dimensional rectilinear distance space through bargaining using the...     

Two-person sequential bargaining behavior with exogenous breakdown

We examine bargaining behavior in a noncooperative game in which players alternate in making and responding to proposals over the division of a given surplus. Although the number of bargaining periods is unlimited and time is not discounted, the bargaining is subject to exogenous breakdown at each period with a fixed probability which is common knowledge. We manipulate three probabilities of break-down in a between-subjects design that allows comparison with previous studies of two-person bargaining with time discounting. Assuming that subjects maximize expected utility, and this utility is measured by monetary payoffs, our results reject both the subgame perfect equilibrium and equal split solutions. Data analyses reveal that a substantial percentage of subjects behave adaptively in that they systematically search for the highest acceptable demands.     

Ambiguity when playing coordination games across cultures

Cultural differences can be a source of ambiguity in coordination games. As players are likely to experience more ambiguity when playing a different culture, we expect players to choose safer strategies. We run experiments with a stag hunt and bargaining coordination game. Using a between-subjects design, we vary the identity of the opponent between someone of the same culture or a different culture. We compare the responses of British and East Asian students at the University of Exeter and show the cultural identity of the opponent by physical appearance. While we find no significant differences between treatments for East Asians, the British choose the safer option in the stag hunt and demand more of the pie in the bargaining game when faced with an opponent from a different culture.

     

Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

Perfect and total altruism across the generations

The traditional formulation of the altruism model has altruistic terms that relate solely to other parties’ felicities from consumption. But if those others are altruistic as well, their altruism benefits are being neglected. Total altruism takes the total utilities of others, rather than their mere felicities, as the basis for altruistic valuations. We assess total altruism in an intergenerational world. Perfect altruism, a concept due to Ramsey (Econ. J. 38(152):543–559, 1928), requires that a generation value itself relative to its successor as it would any two consecutive generations. Total altruism and perfect altruism prove to be incompatible concepts. Total altruism is only meaningful when there is some generational selfishness. The analysis considers both forward-looking and forward and backward-looking altruism.     

Bargaining and Strategic Demand Commitment

On occasion, in multilateral negotiations, interested parties make unilateral demands. Certain agreements need unanimity. However, a lesser degree of consensus may be feasible. In this paper, an alternating demand bargaining game among n players is proposed, which envisages varying consensus requirements and commitment, both crucial in generating a unique and efficient outcome of the bargaining process.     

Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.     

A bargaining model with players' perceptions on the retractability of offers

This paper studies a generalization of Rubinstein's bargaining model with retractable offers. The model incorporates and parameterizes the bargainers' perceptions on the retractability of offers. Our key result characterizes the limiting set of perfect equilibria as the time interval between two consecutive offers tends to zero. In this limit, for any possible players' perceptions on the retractability of offers such that at least one of the players perceives that there is at least a small chance that offers may be retractable, the bargaining game possesses a continuum of perfect equilibria.     

Interpersonal comparisons of utility in bargaining: evidence from a transcontinental ultimatum game

This article presents the experimental results of a “Transcontinental Ultimatum Game” implemented between India and France. We use a standard ultimatum game, but in one treatment, Indian subjects made offers to French subjects (ItoF treatment) and, in another treatment, French subjects made offers to Indian subjects (FtoI treatment). We observed that FtoI treatment bargaining mostly ended up with unequal splits of money in favor of French, while nearly equal splits were the most frequent outcome in ItoF treatment interactions. The experimental results are organized through a standard social reference model, modified for taking into account the different marginal value of money for bargainers. In our model, bargaining is driven by relative standing comparisons between players, occurring in terms of real earnings (that is monetary earnings corrected for a purchasing power factor) obtained in the game. The norm of equity behind the equalization of real earnings is called local equity norm, and contrasted to a global equity norm which would encompass the wealth of players beyond the game. According to what we observed, no beyond-game concern seems to be relevantly endorsed by subjects.     

Implementing egalitarianism in a class of Nash demand games

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to \(1-x\), where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four.     

What price compromise?

This paper identifies, and tests experimentally, a prediction of the Nash bargaining axioms that may appear counterintuitive. The context is a simple bargaining problem in which two players have to agree a choice from three alternatives. One alternative favours one player and a second favours the other. The third is an apparently reasonable compromise, but is in fact precluded as an agreed choice by the Nash axioms. Experimental results show that agreement on this third alternative occurs rather often. Our subjects’ behaviour could be interpreted as the paying of an irrationally high price, according to the Nash axioms, in order to reach a compromise agreement.     

Effects of fixed costs in two-person sequential bargaining

Rubinstein (1982) considered the problem of dividing a given surplus between two players sequentially, and then proposed a model in which the two players alternately make and respond to each other's offers through time. He further characterized the perfect equilibrium outcomes, which depend on the players time preferences and order of moves. Using both equal and unequal bargaining cost conditions and an unlimited number of rounds, two experiments were designed to compare the perfect equilibrium model to alternative models based on norms of fairness. We report analyses of final agreements, first offers, and number of bargaining rounds, which provide limited support to the perfect equilibrium model, and then conclude by recommending a shift in focus from model testing to specification of the conditions favoring one model over another.     

How does socio-economic environment influence the distribution of altruism?

This paper analyzes how socio-economic environment affects the extent of individual altruism and its distribution within a society. We show that if the socio-economic institution that structures interactions between individuals can be represented by a supermodular game, individuals tend to become more homogeneous in terms of altruism as spillover effects increase. This implies that people living close to one another and engaging in joint production, such as irrigation agriculture in a rural village, are more likely to exhibit similar levels of altruism than those living apart and engaging in more or less independent work.     

Rawlsian Nash solutions

We investigate the conditions which guarantee the choice of Rawlsian solutions by players of unequal maximin positions bargaining under Nash rules. The conditions, viz., subsymmetry and the location of the Pareto set, relate to the structure of the utility set,S.     

Joint Beliefs in Conflictual Coordination Games

The traditional solution concept for noncooperative game theory is the Nash equilibrium, which contains an implicit assumption that players probability distributions satisfy t probabilistic independence. However, in games with more than two players, relaxing this assumption results in a more general equilibrium concept based on joint beliefs (Vanderschraaf, 1995). This article explores the implications of this joint-beliefs equilibrium concept for two kinds of conflictual coordination games: crisis bargaining and public goods provision. We find that, using updating consistent with Bayes rule, players beliefs converge to equilibria in joint beliefs which do not satisfy probabilistic independence. In addition, joint beliefs greatly expand the set of mixed equilibria. On the face of it, allowing for joint beliefs might be expected to increase the prospects for coordination. However, we show that if players use joint beliefs, which may be more likely as the number of players increases, then the prospects for coordination in these games declines vis-à-vis independent beliefs.