Torben Tranæs

The Product of Capacities and Belief Functions

Capacities (monotone, non-additive set functions) have been suggested to describe situations of uncertainty. We examine the question of how to define the product of two independent capacities. In particular, for the product of two belief functions (totally monotone capacities), there is a unique minimal product belief function. This is characterized in several ways.

Optimal Workfare with Voluntary and Involuntary Unemployment

This paper addresses the welfare implications of introducing workfare into unemployment benefit policy. We consider a population composed of employed and unemployed workers and of individuals who do not seek employment. Job search behavior is unobservable, which means that voluntarily unemployed individuals can claim unemployment insurance (UI) benefits intended for unemployed workers. As a consequence, pecuniary benefit schemes underinsure workers against unemployment. We show that requiring unproductive activities (workfare) in exchange for UI benefits may generate a Pareto improvement by facilitating better unemployment insurance for workers, and we characterize the situations where this is the case.

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a players assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoners Dilemma in a way that is in accordance with some recent experimental findings.

Progressive Taxation and Wage Setting: Some Evidence for Denmark*

The proposition that a progressive tax system contributes to wage moderation is studied using Danish earnings data disaggregated by occupation, gender and earnings level. Our main conclusions are that income-tax progression affects wage setting, but whether it moderates or exaggerates wage pressure is income dependent. An increase in progressivity reduces the pre-tax earnings of middle-income workers (manual male workers and moderate income earners among both male and female non-manual workers). The reverse is found for high-income earners (non-manual male workers), in that an increase in progressivity tends to raise pre-tax earnings. Finally, there is no significant effect of tax progressivity on the wages of low-income earners. Copyright 2000 by The editors of the Scandinavian Journal of Economics.

Sequential bargaining in a market with one seller and two different buyers

A matching and bargaining model in a market with one seller and two buyers, differing only in their reservation price, is analyzed. No subgame perfect equilibrium exists for stationary strategies. The authors demonstrate the existence of inefficient equilibria in which the low buyer receives the good with large probability, even as friction becomes negligible. They investigate the relationship between the use of Nash and sequential bargaining. Nash bargaining seems applicable only when the sequential approach yields a unique stationary strategy subgame perfect equilibrium.

Expected utility with lower probabilities

An uncertain and not just risky situation may be modeled using so-called belief functions assigning lower probabilities to subsets of outcomes. In this article we extend the von Neumann-Morgenstern expected utility theory from probability measures to belief functions. We use this theory to characterize uncertainty neutrality and different degrees of uncertainty aversion.

Two-Stage Bargaining with Coverage Extension in a Dual Labour Market

This paper studies two-stage bargaining in a simple general equilibrium model with a dual labour market. We analyse the case where agreements reached at the central level in the unionized sector extend beyond this sector, which seems to be a characteristic feature of continental European labour markets. Conditions are identified under which firms and unions have a commonality of interest in extending coverage of a minimum wage to the non-unionized sector of the economy. In many countries, labour markets comprise a primary sector with high non-market clearing wages and job queues, and a secondary sector with market clearing. The latter arises endogenously in our model: it is optimal for the unionized sector to impose a market clearing wage on the non-unionized sector. This suggests that coverage extension can increase welfare.

Decentralized trade with bargaining and voluntary matching

Rubinstein and Wolinsky (1990) study a market with one seller, two buyers, and voluntary matching. Both the competitive outcomepc and the bilateral bargaining outcomepb are possible in subgame perfect equilibrium. We consider two variations. First, if there is a cost larger thanpc−pc to the seller of changing partner,pc is the unique outcome, otherwise no restriction expires. In the second variation the seller makes anε-binding preannouncement of whether he will change buyer after disagreement. Ifε is small there are equilibrium prices close topc. But for anyε, if the discount factor is close to 1, the unique equilibrium price ispc.

Testing the Intransitivity Explanation of the Allais Paradox

This paper uses a two-dimensional version of a standard common consequence experiment to test the intransitivity explanation of Allais-paradox-type violations of expected utility theory. We compare the common consequence effect of two choice problems differing only with respect to whether alternatives are statistically correlated or independent. We framed the experiment so that intransitive preferences could explain violating behavior when alternatives are independent, but not when they are correlated. We found the same pattern of violation in the two cases. This is evidence against intransitivity as an explanation of the Allais Paradox. The question whether violations of expected utility are mainly due to intransitivity or to violation of independence is important since it is exactly on this issue the main new decision theories differ.

On the Efficiency of Decentralized Exchange with Resale Possibilities

This paper studies decentralized exchange by bilateral matching and bargaining when resale is possible. Decentralized exchange involves the risk that goods and services may be allocated inefficiently; if low-valuation buyers consume while high-valuation buyers do not, then social welfare is reduced. If resale is possible and transaction costs are negligible, we would nevertheless expect an efficient allocation to result from decentralized exchange. This paper suggests that this depends on the nature of the commodity; while the allocation of a durable good will be efficient, the allocation of a consumable good need not. Copyright 1999 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.