We introduce a new cooperative stability concept, *absence-proofness *(AP). Given a TU game (N,v), and a solution well defined for all subsocieties, a group of people S⊆N may benefit by partially seceding from cooperation. T⊆S stays out, and collects its stands alone benefits while S∖T receives its allocation specified by the solution at the reduced problem where only N∖T is present. We call a solution manipulable if S can improve upon its allocation in the original problem by such a maneuver, and solutions that are immune to such manipulations are called absence-proof. We show that population monotonicity (PM) implies AP, and AP implies separability. In minimum cost spanning tree problems, by replacing PM with AP, we propose a family of solutions that are easy to compute and more responsive than the well-known Folk solution to the asymmetries in the cost data, keeping all its fairness properties.

We find that the answer to the open question of whether there is a continuous core solution that satisfies coalitional monotonicity in the class of convex games is yes. We prove that the SD-prenucleolus is a continuous core solution that satisfies coalitional monotonicity for convex games, a class of games widely used to model economic situations.

We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each k∈N={0,1,…}k∈N={0,1,…} we introduce an effective reward function, called k-total. For k=0k=0 and 1 this function is known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case. For all k, we prove the existence of a saddle point which can be realized by uniformly optimal pure stationary strategies. We also demonstrate that k-total reward games can be embedded into (k+1)(k+1)-total reward games.

We set up a laboratory experiment to investigate systematically how varying the magnitude of outside options—the payoffs that materialize in case of a bargaining breakdown—of proposers and responders influences players’ demands and game outcomes (rejection rates, payoffs, efficiency) in ultimatum bargaining. We find that proposers as well as responders gradually increase their demands when their respective outside option increases. Rejections become more likely when the asymmetry in the players’ outside options is large. Generally, the predominance of the equal split decreases with increasing outside options. From a theoretical benchmark perspective we find low predictive power of equilibria based on self-regarding preferences or inequity aversion. However, proposers and responders seem to be guided by the equity principle while they apply equity rules inconsistently and self-servingly.

We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players’ behavior deviates from rationality, but rather, on players’ higher-order beliefs about the frequency of such deviations. We assume that there exists a probability *p* such that all players believe, with at least probability *p*, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of *p*-rational outcomes, which we define and characterize for arbitrary probability *p*. We then show that this set varies continuously in *p* and converges to the set of correlated equilibria as *p* approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The *p*-rational outcomes are easy to compute, also for games of incomplete information. Importantly, they can be applied to observed frequencies of play for arbitrary normal-form games to derive a measure of rationality *p** that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization.

We propose a new notion of farsighted pairwise stability for dynamic network formation which includes two notable features: consideration of intermediate payoffs and cautiousness. This differs from existing concepts which typically consider either only immediate or final payoffs, and which often require that players are optimistic in any environment without full communication and commitment. For arbitrary (and possibly heterogeneous) preferences over the process of network formation, a non-empty cautious path stable (CPS) set of networks always exists. Furthermore, some general relationships exist between CPS and other farsighted concepts.

This paper axiomatically studies the equal split-off set (cf. Branzei et al. (Banach Center Publ 71:39–46, 2006)) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (Econometrica 57:615–635, 1989) solution for convex games. By deriving several characterizations, we explore consistency of the equal split-off set on the domains of exact partition games and arbitrary games.

Recently developed toy models for the mean-field games of corruption and botnet defence in cyber-security with three or four states of agents are extended to a more general mean-field-game model with 2d states, d ∈ N. In order to tackle new technical difficulties arising from a larger state-space we introduce new asymptotic regimes, namely small discount and small interaction asymptotics. Moreover, the link between stationary and time-dependent solutions is established rigorously leading to a performance of the turnpike theory in a mean-field-game setting.

We consider the game of proper NIM, in which two players alternately move by taking stones from *n* piles. In one move a player chooses a proper subset (at least one and at most n−1n−1) of the piles and takes some positive number of stones from each pile of the subset. The player who cannot move is the loser. Jenkyns and Mayberry (Int J Game Theory 9(1):51–63, 1980) described the Sprague–Grundy function of these games. In this paper we consider the so-called selective compound of proper NIM games with certain other games, and obtain a closed formula for the Sprague–Grundy functions of the compound games, when n≥3n≥3. Surprisingly, the case of n=2n=2 is much more complicated. For this case we obtain several partial results and propose some conjectures.

We consider the fair division of a set of indivisible goods where each agent can receive more than one good, and monetary transfers are allowed. We show that if there are at least three goods to allocate, no efficient solution is population monotonic (PM) on the superadditive Cartesian product preference domain, and the Shapley solution is not PM even on the submodular domain. Moreover, the incompatibility between efficiency and PM prevails in the case of at least four goods on the subadditive Cartesian product domain. We also show that in case there are only two goods to allocate, the Shapley solution and the constrained egalitarian solution are PM on the subadditive preference domain but not on the full preference domain. For the two-good case, we provide a new tool (the hybrid solutions) to construct efficient solutions that are PM on the entire monotone preference domain. The hybrid Shapley solution and the hybrid constrained egalitarian solution are two important examples of such solutions.

In 1964 Shapley observed that a matrix has a saddle point in pure strategies whenever every its (Formula presented.) submatrix has one. In contrast, a bimatrix game may have no pure strategy Nash equilibrium (NE) even when every (Formula presented.) subgame has one. Nevertheless, Shapley’s claim can be extended to bimatrix games as follows. We partition all (Formula presented.) bimatrix games into fifteen classes (Formula presented.) depending only on the preferences of two players. A subset (Formula presented.) is called a NE-theorem if a bimatrix game has a NE whenever it contains no subgame from t. We suggest a method to construct all minimal (that is, strongest) NE-theorems based on the procedure of joint generation of transversal hypergraphs given by a special oracle. By this method we obtain all (six) strongest NE-theorems. Let us remark that the suggested approach, which may be called “math-pattern recognition”, is very general: it allows to characterize completely an arbitrary “target” in terms of arbitrary “attributes”.

A tournament can be represented as a set of candidates and the results from pairwise comparisons of the candidates. In our setting, candidates may form coalitions. The candidates can choose to fix who wins the pairwise comparisons within their coalition. A coalition is winning if it can guarantee that a candidate from this coalition will win each pairwise comparison. This approach divides all coalitions into two groups and is, hence, a simple game. We show that each minimal winning coalition consists of a certain uncovered candidate and its dominators. We then apply solution concepts developed for simple games and consider the desirability relation and the power indices which preserve this relation. The tournament solution, defined as the maximal elements of the desirability relation, is a good way to select the strongest candidates. The Shapley–Shubik index, the Penrose–Banzhaf index, and the nucleolus are used to measure the power of the candidates. We also extend this approach to the case of weak tournaments.

In this paper we examine the effects of valence in a continuous spatial voting model with two incumbent candidates and a potential entrant. All candidates are rank-motivated. We first consider the case where the low valence incumbent (LVC) and the entrant have zero valence, whereas the valence of the high valence incumbent (HVC) is positive. We show that a sufficiently large valence of HVC guarantees a unique equilibrium, where the two incumbents prevent the entry of the third candidate. We also show that an increase in valence allows HVC to adopt a more centrist policy position, while LVC selects a more extreme position. We also examine the existence of equilibrium for the cases where the LVC has higher or lower valence than the entrant.