Hannu Salonen

A solution for two-person bargaining problems

Everyday bargaining problems are often solved by tossing a coin. A solution for two-person bargaining problems is axiomatized, which is a Pareto-optimal generalization of this coin tossing method. The super-additive solution of Perles and Maschler is also shown to be a generalization of this method. Various properties of our solution are studied, including continuity and risk sensitivity, and compared with properties of other solutions discussed in the literature.

The representative Nash solution for two-sided bargaining problems

Abstract An n -person bargaining situation is two-sided when participants of bargaining are divided into two groups and their preferences over bargained outcomes are exactly opposite to each other. This is so when the issue on the bargaining table is represented by a one dimensional set and people’s preferences are monotonically increasing in one group and monotonically decreasing in the other group. In this paper a solution for two-sided problems called the Representative Nash solution is introduced and axiomatized. A strategic bargaining model is constructed such that the unique stationary subgame perfect equilibrium outcome corresponds to the Representative Nash solution.

Decomposable solutions for N — person bargaining games

Abstract Two solutions for n-person bargaining games are defined and axiomatized, which exhibit the so called “decomposability property”. One of the solutions extends the two-person Kalai-Smorodinsky solution to n-person games. The other is the Raiffa solution.

Partially monotonic bargaining solutions

The purpose of the paper is to study partially monotonic solutions for two-person bargaining problems. Partial monotonicity relates to the uncertainty a player has about the solution before bargaining. If the minimum utility a player can expect is greater in game T than in game S, and if T contains more alternatives than S, this may bring him to expect that his utility at the solution is greater in T than in S. Partially monotonic solutions reflect these expectations.One partially monotonic solution is axiomatized. The axioms of symmetry and independence of linear transformations are not explicitly assumed, although the solution has also these properties. The Kalai-Smorodinsky solution is shown to be the only continuous partially monotonic solution.

Minimum norm solutions for cooperative games

A solution f for cooperative games is a minimum norm solution, if the space of games has a norm such that f(v) minimizes the distance (induced by the norm) between the game v and the set of additive games. We show that each linear solution having the inessential game property is a minimum norm solution. Conversely, if the space of games has a norm, then the minimum norm solution w.r.t. this norm is linear and has the inessential game property. Both claims remain valid also if solutions are required to be efficient. A minimum norm solution, the least square solution, is given an axiomatic characterization.

On the existence of Nash equilibria in large games

We study the existence of Nash equilibria in games with an infinite number of players. We show that there exists a Nash equilibrium in mixed strategies in all normal form games such that pure strategy sets are compact metric spaces and utility functions are continuous. The player set can be any nonempty set.

On continuity of Arrovian social welfare functions

We study continuity properties of Arrovian social welfare functions in the infinite population framework. We show that continuous welfare functions satisfying unanimity and independence of irrelevant alternatives are dictatorial. Weak anonymity is shown to be incompatible with continuity and unanimity: every continuous weakly anonymous social welfare function must be a constant function.

Egalitarian solutions for n-person bargaining games

Abstract In this paper a new axiomatization of the α-egalitarian solutions is proposed. The axioms are Weak Pareto Optimality, Homogeneity and Translation Invariance, Kuratowski Continuity, and Disagreement Point Concavity. In this axiomatization, Individual Rationality need not be assumed explicitly. Kuratowski Continuity cannot be replaced by Hausdorff Continuity even if Individual Rationality is assumed.

Continuity properties of bargaining solutions

Three different concepts of continuity of bargaining solutions are examined: Pareto continuity, Hausdorff continuity, and Kuratowski continuity. A new axiomatic characterization of the Nash solution is proposed. In this axiomatization, Kuratowski continuity plays a major role.

Equilibria and centrality in link formation games

We study non-cooperative link formation games in which players have to decide how much to invest in connections with other players. The relationship between equilibrium strategies and network centrality measures are investigated in games where there is a common valuation of players as friends. The utility from links is a weighted sum of Cobb–Douglas functions, the weights representing the common valuation. If the Cobb–Douglas functions are bilinear and the link formation cost is not too high, then indegree, eigenvector centrality, and the Katz–Bonacich centrality measure put the players in opposite order than the common valuation. The same result holds for non-negligible link formation costs if the Cobb–Douglas functions are separately concave but not jointly concave. If the Cobb–Douglas functions are strictly concave, then at the interior equilibrium these measures order the players in the same way as the common valuation.