Fall Back Equilibrium

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.strategic game;equilibrium refinement;blocked action;fall back equilibrium

A Silent Battle over a Cake

The division of a cake by n players is modeled as a game of timing. We show that such games admit a unique Nash equilibrium.Game of timing;Nash equilibrium

A Geometric Characterisation of the Compromise Value

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover.For this, we introduce the value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games.geometry;games;bankruptcy;core

Compromise Solutions for Bankruptcy Situations with References

This paper deals with bankruptcy situations in which in addition to the claims, an exogenously given reference point for the allocation of the estate is present.We introduce and analyse two types of compromise solutions and show that they coincide with the T value of two corresponding TU games.We apply our solutions to a real-life case of allocating university money to degree courses.bankruptcy;allocation;t-value;games

Transfers, Contracts and Strategic Games

This paper analyses the role of transfer payments and strategic con- tracting within two-person strategic form games with monetary pay- offs. First, it introduces the notion of transfer equilibrium as a strat- egy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail. The second part of the paper introduces, also within the setting of finite games, contracting on monetary transfers as an explicit strategic option, resulting in an associated two-stage contract game. In the first stage of the contract game each player has the option of proposing transfer schemes for an arbitrary collection of outcomes. Only if the players fully agree on the entire set of transfer proposals, the payoffs of the game to be played in the second stage are modified accordingly. The main results provide explicit characterisations of the sets of payoff vectors that are supported by Nash equilibrium and virtual subgame perfect equilibrium, respectively.monetary transfer scheme;transfer equilibrium;contract game;virtual subgame perfect equilibrium;Folk theorems