Selfishness Level of Strategic Games

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is $c/(b(n-1)-c)$, where $b$ and $c$ are the benefit and cost for cooperation, respectively, that of the $n$-players public goods game is $(1-\frac{c}{n})/(c-1)$, where $c$ is the public good multiplier, and that of the Traveler's Dilemma game is $\frac{1}{2}(b-1)$, where $b$ is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game, Tragedy of the Commons, and Bertrand competition is infinite.Comment: 34 page

Demography and the tragedy of the commons

Individual success in group-structured populations has two components. First, an individual gains by outcompeting its neighbors for local resources. Second, an individual's share of group success must be weighted by the total productivity of the group. The essence of sociality arises from the tension between selfish gains against neighbors and the associated loss that selfishness imposes by degrading the efficiency of the group. Without some force to modulate selfishness, the natural tendencies of self interest typically degrade group performance to the detriment of all. This is the tragedy of the commons. Kin selection provides the most widely discussed way in which the tragedy is overcome in biology. Kin selection arises from behavioral associations within groups caused either by genetical kinship or by other processes that correlate the behaviors of group members. Here, I emphasize demography as a second factor that may also modulate the tragedy of the commons and favor cooperative integration of groups. Each act of selfishness or cooperation in a group often influences group survival and fecundity over many subsequent generations. For example, a cooperative act early in the growth cycle of a colony may enhance the future size and survival of the colony. This time-dependent benefit can greatly increase the degree of cooperation favored by natural selection, providing another way in which to overcome the tragedy of the commons and enhance the integration of group behavior. I conclude that analyses of sociality must account for both the behavioral associations of kin selection theory and the demographic consequences of life history theory

The Economics of Corporate Tax Selfishness

This paper offers an economics perspective on corporate tax noncompliance. It first reviews what is known about the extent and nature of corporate tax noncompliance and the resources devoted to enforcement. It then addresses the supply of corporate noncompliance -- the industrial organization of the tax shelter industry -- as well as the demand for corporate tax noncompliance, focusing on how the standard Allingham-Sandmo approach needs to be modified when applied to public corporations. It then discusses the implications of a supply-and-demand approach for the analysis of the incidence and efficiency cost of corporate income taxation, and the very justification for a separate tax on corporation income. Along the way it addresses policy proposals aimed at increased disclosure of corporate tax activities to both the IRS and to the public.

Strategy intervention for the evolution of fairness

Masses of experiments have shown individual preference for fairness which seems irrational. The reason behind it remains a focus for research. The effect of spite (individuals are only concerned with their own relative standing) on the evolution of fairness has attracted increasing attention from experiments, but only has been implicitly studied in one evolutionary model. The model did not involve high-offer rejections, which have been found in the form of non-monotonic rejections (rejecting offers that are too high or too low) in experiments. Here, we introduce a high offer and a non-monotonic rejection in structured populations of finite size, and use strategy intervention to explicitly study how spite influences the evolution of fairness: five strategies are in sequence added into the competition of a fair strategy and a selfish strategy. We find that spite promotes fairness, altruism inhibits fairness, and the non-monotonic rejection can cause fairness to overcome selfishness, which cannot happen without high-offer rejections. Particularly for the group-structured population with seven discrete strategies, we analytically study the effect of population size, mutation, and migration on fairness, selfishness, altruism, and spite. A larger population size cannot change the dominance of fairness, but it promotes altruism and inhibits selfishness and spite. Intermediate mutation maximizes selfishness and fairness, and minimizes spite; intermediate mutation maximizes altruism for intermediate migration and minimizes altruism otherwise. The existence of migration inhibits selfishness and fairness, and promotes altruism; sufficient migration promotes spite. Our study may provide important insights into the evolutionary origin of fairness.Comment: 15 pages, 7 figures. Comments welcom

Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.Comment: 30 pages, 7 figure

The nature of human altruism

Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene–culture co-evolution.altruism, selfishness, human altruism, evolution

A Defense of Egoism

This paper defends the strong thesis of ethical egoism, the view that self-interest is the exclusive standard of morally right action. The method of defense is that of reflective equilibrium, viz., back and forth reflection on intuitive judgments in particular cases and the principles that seem to explain our judgments, with the goal of aligning the two. The defense proceeds in three steps. First, I define what selfishness is and characterize what selfishness looks like in real life; an accurate depiction of selfishness will show that selfishness, at least generally, is morally attractive. Second, I defend the view that helping others and not helping others is morally right when and because doing so serves one’s self-interest. Third, I defend the same position in regard to harming and not harming others