On loss aversion in bimatrix games

In this paper we study three different types of loss aversion equi-libria in bimatrix games. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points – points below which they consider payoffs to be losses – are endoge-nous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000) under the name of ‘myopic loss aversion equilibrium’. There, the players’ reference points depend on the beliefs about their opponents ’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference point is now only based on the carrier of the players’ beliefs, not on the exact prob-abilities. In the third, the safety level loss aversion equilibrium, this dependence is completely dispensed with. Finally, we do a compara-tive statics analysis of all three equilibrium concepts in 2 × 2 bimatrix games. The results indicate that a player, under some conditions, benefits from his opponent falsely believing he is loss averse

On loss aversion in bimatrix games

ABSTRACT. In this article three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points-points below which they consider payoffs to be lossesare endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000; Int. J. Game Theory 29(2):269) under the name of 'myopic loss aversion equilibrium.' There, the players' reference points depend on the beliefs about their opponents' strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference points are only based on the carriers of the strategies, not on the exact probabilities. In the third type, the safety level loss aversion equilibrium, the reference points depend on the values of the own payoff matrices. Finally, a comparative statics analysis is carried out of all three equilibrium concepts in 2 × 2 bimatrix games. It is established when a player benefits from his opponent falsely believing that he is loss averse

Behavioural decisions and welfare

We study decision problems where (a) preference parameters are de.ned to include psychological/moral considerations and (b) there is a feedback effect from chosen actions to preference parameters. In a standard decision problem the chosen action is required to be optimal when the feedback effect from actions to preference parameters is fully taken into account. In a behavioural decision problem the chosen action is optimal taking preference parameters as given although chosen actions and preference parameters are required to be mutually consistent. Our framework unifes seemingly disconnected papers in the literature. We characterize the conditions under which behavioural and standard decisions problems are indistinguishable: in smooth settings, the two decision problems are generically distinguishable. We show that in general, revealed preferences cannot be used for making welfare judgements and we characterize the conditions under which they can inform welfare analysis. We provide an existence result for the case of incomplete preferences. We suggest novel implications for policy and welfare analysis

Behavioural decisions & policy

We study the public policy implications of a model in which agents do not fully internalize all the conscequences of their actions. Such a model uni…es seemingly disconected models with behavioral agents. We evaluate the scope of paternalistic and libertarian-parternalistic policies in the light of our model, and propose an alternative type of approach, called soft-libertarian, which guides the decision makers in the internalization of all the conscequences of their actions. Psychotherapy is one example of a soft-libertarian policy. Moreover, we show that in our behavioral framework, policies that increase the set of opportunities or provide more information to the agent may not longer be individual welfare improving

The Kalai-Smorodinsky Solution with Loss Aversion

We consider bargaining games under the assumption that bargainers are loss averse, i.e. experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on a solution. Given a bargaining game, we say outcome z is self-supporting under a given bargaining solution, whenever transforming the game using outcome z as reference point, yields a transformed game in which the solution is z.We show that n-player bargaining games have a unique self-supporting outcome under the Kalai-Smorodinsky (KS) solution. We define a bargaining solution, giving exactly this outcome, and characterize it by the standard axioms of Scale Invariance [SI], Individual Monotonicity [IM], and Strong Individual Rationality [SIR], and a novel axiom called Proportional Concession Invariance [PCI].A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome, does not change this outcome.microeconomics ;

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201

Behavioural Decisions and Policy

We study the public policy implications of a model in which agents do not fully internalize all the conscequences of their actions. Such a model unifies seemingly disconected models with behavioral agents. We evaluate the scope of paternalistic and libertarian-parternalistic policies in the light of our model, and propose an alternative type of approach, called soft-libertarian, which guides the decision makers in the internalization of all the conscequences of their actions. Psychotherapy is one example of a soft-libertarian policy. Moreover, we show that in our behavioral framework, policies that increase the set of opportunities or provide more information to the agent may not longer be individual welfare improving.Behavioral Decisions, Revealed Preferences, Normative Preferences, Paternalism, Soft-Libertarian, Autonomy, Psychotherapy

Behavioral Decisions and Policy

We study the public policy implications of a model in which agents do not fully internalize all the conscequences of their actions. Such a model uni es seemingly disconected models with behavioral agents. We evaluate the scope of paternalistic and libertarian-parternalistic policies in the light of our model, and propose an alternative type of approach, called soft-libertarian, which guides the decision makers in the internalization of all the conscequences of their ac- tions. Psychotherapy is one example of a soft-libertarian policy. Moreover, we show that in our behavioral framework, policies that increase the set of oppor- tunities or provide more information to the agent may not longer be individual welfare improving.Behavioral Decisions;Revealed Preferences;Normative Preferences;Paternalism;Soft-Libertarian;Autonomy;Psychotherapy