Set-valued solution concepts using interval-type payoffs for interval games

Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core and the interval stable sets for cooperative interval games, are introduced and studied. The main results contained in the paper are a necessary and sufficient condition for the non-emptiness of the interval core of a cooperative interval game and the relations between the interval core, the interval dominance core and the interval stable sets of such a game.     

Coalition formation in general NTU games

A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players' opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players' outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.     

The hybrid equilibria and core selection in exchange economies with externalities

This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.     

COMMON‐ENEMY EFFECTS: MULTIDISCIPLINARY ANTECEDENTS AND ECONOMIC PERSPECTIVES

A disparate literature hypothesizes what can broadly be described as the common‐enemy effect: the fact that the interaction with a common enemy (formed by Nature, an individual, or a group) increases cooperation. This review identifies the multidisciplinary antecedents of this effect, and then distinguishes between several strands of literature applying noncooperative game theory to account for it. A first strand argues that the threat posed by a common enemy makes each player's cooperative effort more critical. In a second strand a behavioral common‐enemy effect caused by group interaction is studied experimentally. A third strand models the common‐enemy effect as the formation of a coalition of players against another player in a contest. A fourth strand formalizes the principle that the ‘enemy of my enemy is my friend’, either in a model of social relations, interdependent altruistic preferences, or indirect reciprocity in repeated games. The connections between these strands of literature are investigated, and questions for future research are proposed.     

RECENT ADVANCES IN OLIGOPOLY THEORY FROM A GAME THEORY PERSPECTIVE

Abstract. This paper surveys the contribution that recent developments in game theory have made to the understanding of oligopoly theory. It is argued that conventional models suffer from the problem that there are a number of solution concepts offered with little guidance as to which should be selected, and this is related to the static nature of the models employed. One important development in game theory has been the analysis of repeated games, and when applied to oligopoly theory this suggests that outcomes may be more cooperative than conventional theory suggests. Related to this is the requirement that firms employ credible threats to punish cheating from cooperative outcomes, and the paper examines the extent to which imperfect information may restrict the scope of firms to employ such punishments. One way in which firms may seek to make threats credible is through strategic investments, for example in production capacity, and the paper explores how competition over price or output is integrated with competition over instruments for strategic investment.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Trade unions,collective bargaining and macroeconomic performance: a review

Coordination through collective bargaining is recognised as an influential determinant of labour market outcomes and macroeconomic performance. This article provides a systematic review of the empirical literature on the subject. What emerges from the review is that it is different types and coverage of bargaining coordination, rather than cross‐country variation in trade union density, that matter for economic performance. High levels of bargaining coverage tend to be associated with relatively poor economic performance, but this adverse relationship can be at least mitigated by high levels of bargaining coordination. In the absence of formal bargaining arrangements, economies often develop informal bargaining mechanisms whose effects are similar to those arising from formal bargaining provided they both operate at similar levels of coordination. The consequences of labour market coordination or absence thereof depend on the monetary policy regime as non‐accommodating monetary policy can eliminate some of the adverse unemployment consequences otherwise associated with industry‐level collective bargaining. Finally, bargaining coordination seems to matter most in times of rapid economic change rather than under more stable conditions. Overall, we conclude that it is the total ‘package’ of (formal and informal) labour market institutions that matters for the performance of the economy rather than unionisation as such or individual aspects of unionism.     

Undermining or reframing collective bargaining? Variable pay in two sectors compared

Although it is widely presumed that variable payments systems (VPS) such as individual merit and profit‐related pay are corrosive of collective bargaining, the actual relationship between the two remains little explored. Drawing on company case studies from retail banking and machinery and equipment, this article finds that collective bargaining can variously be reconfigured – as over individual merit pay in the banks; extended to cover local bonus arrangements, evident in instances in both sectors; or lose its purchase on a significant proportion of earnings – as with management‐determined profit‐related bonus in both sectors. In terms of the implications for collective bargaining, much therefore depends on the type of VPS.     

A formulation of the aggregation problem in terms of coalition and bargaining theory

The object of this paper is to demonstrate in economic terms the equivalence of the problem of aggregation in input-output analysis with coalition and bargaining problems. Depending on the specific norm for aggregation it is shown that the aggregation criterion and the coalition forming criterion in an n-person game leads to a broadly similar situation in the market sense given that the market operates to that criterion. It is also shown that a mathematical analogue to this formulation may be obtained via the techniques of geometric programming.     

Coalition structure values in differential information economies: is unity a strength?

The coalition structure (CS) value, introduced by Owen [G. Owen, Values of games with a priori unions, in: Essays in Mathematical Economics and Game Theory, Springer Verlag, Berlin, 1977] and Hart and Kurz [Econometrica 51 (1983) 1047], generalizes the Shapley value to social situations where coalitions form for the purpose of bargaining. This paper introduces the CS value to economies with differential information. We show that the private CS values exists and is Bayesian incentive compatible. Moreover, we construct examples that go against the intuitive viewpoint that “unity is strength”. In particular, we consider a three-person economy in which two agents bargain as a unit against the third agent. We show that bargaining as a unit is advantageous if and only if information is complete. This result sheds new light on bargaining under differential information.     

Reject and renegotiate: The Shapley value in multilateral bargaining

This paper investigates three distinctive and intuitive renegotiation bargaining protocols that all yield the Shapley value as the unique subgame perfect equilibrium outcome. These protocols, built on the multi-bidding procedure of Pérez-Castrillo and Wettstein (2001), allow more freedom in multilateral bargaining where rejected players can further negotiate and form coalitions. The self-duality of the Shapley value plays a key role in the second and third results. Moreover, these renegotiation protocols allow an actual play along the equilibrium path to restore the Shapley value in case of a ‘mistake’ made before.     

Cooperative game with nondeterministic returns

We study a non-traditional cooperative game where returns from coalitions are nondeterministic. The long-standing concept of core can be generalized to reflect players’ contentment with their allocations. It is now imperative to formalize the restrictions, such as those pertaining to information, on allocations. The latter are also at times more conducive to fractional representations. With probabilistic structures added, nondeterministic returns become random variables, utility functions attain risk-attitude connotations, and the timing of players’ allocation resolutions gains significance. Under various conditions for utility functions, we show how various core concepts of the general game can be related to its traditionally defined auxiliaries. These developments help pave the way for our illustrations, within two distinct settings, that players’ increased risk aversion would promote the formation of the grand coalition.     

Collective bargaining and new work regimes: ‘too important to be left to bosses’

The formal negotiations process remains perhaps the least‐studied moment of collective bargaining. Drawing on ideal types of ‘distributive’ and ‘integrative’ bargaining and the ‘formal/informal’ distinction, this article reports non‐participant observation and ethnographic research into the negotiations process that enabled a change agreement in a British multinational, hereafter anonymised as FMCG. Informal bargaining relations provided the backdrop to—and emerged within—the formal negotiations process. Formal bargaining established new employment contracts based on a simplified internal labour market and generated the joint governance processes to enable and regulate the change process. Neither management nor union strategy was wholly derived from rational, interest‐based positions. The negotiations process was essential to strategy formation and to the emergence of sufficient ‘integrative’ bargaining for all parties to devise and approve new processual institutions and norms to deliver a more flexible labour process and to restore the long‐run viability for ‘distributive’ bargaining.     

Political institutions and economic growth

We analyze the impact of micro-founded political institutions on economic growth in an overlapping-generations economy, where individuals differ in preferences over a public good (as well as in age). Labour- and capital taxes finance the public good and a public input. The benchmark institution is a parliament, where all decisions are taken. Party entry, parliamentary composition, coalition formation, and bargaining are endogenous. We compare this constitution to delegation of decisionmaking, where a spending minister (elected in parliament or appointed by the largest party). Delegation of decisionmaking tends to yield lower growth, mainly due to the occurrence of production inefficiency.     

Stable and efficient coalitional networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with her coalition members and with individuals outside her coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concepts of strong stability and of contractual stability. Contractual stability imposes that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. Requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and efficiency. Moreover, this new framework can provide insights that one cannot obtain if coalition formation and network formation are tackled separately and independently.     

两级供应链中的利益分配

供应链中的利益分配问题是理论界和企业界都十分关注的问题,它关系到供应链联盟的稳定性,关系到企业之间利润分配的公平性。本文介绍了合作对策的一些基本概念;Shapley值求解合作对策的基本原理和公式,以及应用Shapley值方法求解两级供应链中的利益分配问题。     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

Generalized coalitions and bargaining sets

We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin, 1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation.     

Time horizons matter: the hazard rate of coalition governments and the size of government

This study examines how coalition governments affect the size of government, measured by total central government expenditure as a share of GDP. Existing studies suggest that the presence of multiple political parties within ruling coalitions generate common pool resource problems or bargaining inefficiencies which, in turn, leads to more government spending when coalition governments are in office. We demonstrate that coalition governments have shorter time horizons than single party governments and use that finding to motivate a simple formal model. The model shows that coalition governments have greater incentives to increase government spending because of a lower discount factor in office. Results from empirical models estimated on a global sample of 111 democracies between 1975 and 2007 provide strong statistical support for the aforementioned theoretical prediction. The empirical results remain robust when we control for alternative explanations, employ different estimation techniques, and use different measures of government spending.     

Rationality of bargaining solutions

The aim of this paper is to obtain the rationality of two-person bargaining solutions by imposing usual assumptions in cooperative bargaining theory. In particular, it is proved that the conjunction of Independence of Irrelevant Alternatives and either Pareto Continuity or Strong Monotonicity implies this rationality.