Online research in philosophy

The replicator dynamics have been used to study the evolution of a population of rational agents playing the Nash bargaining game, where an individual's "fitness" is determined by an individual's success in playing the game. In these models, a population whose initial conditions was randomly chosen from the space of population proportions converges to a state of fair division approximately 62% of the time. (Higher rates of convergence to final states of fair division can be obtained by introducing artificial correlations into the models.) Spatial models of the Nash bargaining game exhibit considerably more robust convergence properties. These properties are considered at length, and a sufficient condition for convergence to fair division is proved.

Ainslie is correct in arguing that the force of commitments partly depends on the predictive role of present action, but this claim can be supported independently of the analogy with interpersonal bargaining. No matter whether we conceive of the parties involved in the bargaining as interests or transient selves, the picture of the will as a competitive interaction among these parties is unconvincing.

Philosophical disagreement about justice ranges over at least two questions. The most immediate is a substantial question, concerning the conditions under which particular distributive arrangements can be said to be just or unjust. The second, deeper, question concerns the nature of justice itself. What is justice? Here we can distinguish three views. First, justice as mutual advantage sees justice as essentially a matter of the outcome of a bargain. There are times when two parties can both be better off by making some sort of agreement. Justice, on this view, concerns the distribution of the benefits and burdens of the agreement. Second, justice as reciprocity takes a different approach, looking not at bargaining but at the idea of a fair return or just price, attempting to capture the idea of justice as equal exchange. Finally justice as impartiality sees justice as ‘taking the other person’s point of view’ asking ‘how would you like it if it happened to you?’ Each model has significantly different consequences for the question of when issues of justice arise and how they should be settled. It is interesting to consider whether any of these models of justice could regulate behaviour between non-human animals.

Evolutionary game theoretic accounts of justice attempt to explain our willingness to follow certain principles of justice by appealing to robustness properties possessed by those principles. Skyrms (1996) offers one sketch of how such an account might go for divide-the-dollar, the simplest version of the Nash bargaining game, using the replicator dynamics of Taylor and Jonker (1978). In a recent article, D'Arms et al. (1998) criticize his account and describe a model which, they allege, undermines his theory. I sketch a theory of evolutionary explanations of justice which avoids their methodological criticisms, and develop a spatial model of divide-the-dollar with more robust convergence properties than the models of Skyrms (1996) and D'Arms et al. (1998).

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.

It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the form 'each according to her basic needs and above this level according to her relative bargaining power'. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls' original position.