Coalition formation theory deals with the analysis of one or more groups of agents, called coalitions, that get together to jointly determine their actions. It is related both to cooperative and non-cooperative games, as the key concept of this theory, coalition, can be defined as a group of agents which coordinates agreements among its members, while it interacts non-cooperatively with its non-members.

Although a coalition, once formed, is cooperative, its creation can take place in a non-cooperative way. Essentially, one may distinguish two main aspects of coalition formation theories.

One of them concerns the formation of groups, that is, the process through which a coalition comes together to coordinate its actions. Another aspect of coalition formation theories involves the enforcement of group actions as the equilibrium of an appropriate game. Skip to main content. Structure Partners Scientific Board Secretariat.

Search form Search. Coalition Formation Theory. Working paper. Alternative representation of semivalues, the inverse problem and coalitional rationality.

Irinel Dragan and Pierre Dehez. Paths to stability for overlapping group structures. Approximate Coalitional Equilibria in the Bipolar World. Andrei Golman, Daniil Musatov. From theory to application. Transfers, self-enforcing agreements and climate cooperation.

Common ranking and stability of overlapping coalitions. Constitutions and groups. Immunity to credible deviations from the truth. Collusive Agreements in Vertically Differentiated Markets. Marco A. Sareh Vosooghi. On the nonemptiness of approximate cores of large games. Nizar Allouch, Myrna Wooders. Locating a public good on a sphere.To browse Academia. Skip to main content. Log In Sign Up. Download Free PDF. Keshab Bhattarai. Dynamic Poverty game is proposed for alleviation of poverty that requires cooperation from tax payers, transfer recipients and the democratic government and the international community.

These concepts are applied to analyse how the incorporation of growth pact in the constitution can set a mechanism for cooperative solution required for peaceful and prosperous Nepal without harmful conflicts that had upset the growth process over the years. Bhattarai hull. Dominants firms competing for a market share, political parties contesting for power and research and scientific discoveries aimed for path-breaking innovations are influenced by decision taken by others.

In all these circumstances there are situations where collective efforts rather than individual ones generate the best outcome for the group as a whole and for each individual members of the group. Concepts of bargaining, coalition and repeated games developed over years by economists such as CournotBertrandEdgeworth von Neumann and Morgenstern and Nashis developing very fast in recent years following works of KuhnShapley ,Shelten Aumman ScarfShapley and ShubicHarsanyiSpenceHurwiczMyersonMaskin and TiroleKrepsFundenberg and Tirole and BinmoreRubinstein Sutton Cho and Kreps Sobel Machina Riley McCormickGhosal and Morelli These have generated models that can be applied to analyse the relative gains from coalitions rather than without these coalitions.

The major objective of this paper is to apply these concepts to analyse the rationality or irrationality of choices made by political parties in Nepal in process of transforming its political economic system aiming to create a peaceful and prosperous economy like her neighbours India and China.

This is further refinement of the solutions discussed on bargaining and political economy and general equilibrium models analysed in Bhattarai and When a cooperation is achieved there is a question on whether such coalition is stable or not. There are always incentives at least for one of the player to cheat from this cooperative agreement in order to raise its own share of the gain.

However, it is unlikely that any player can fool all other at all the times. Others will discover such cheating sooner ot later. Therefore a peaceful solution requires credibility and a punishment mechanism by which any party that tries to cheat on the agreement is punished unless its reforms are uncooperative behaviours to others.

### Coalition Formation Theory

In the context of Nepal abolition of absolute monarchy required cooperation of all parties which was achieved under the November agreeement concurred in New Delhi.

Consequences of this agreement were phenomenal in terms of transformation of power among political parties. In the next stage of the game the only unifying objective of such cooperation can be the alleviation of mass scale poverty and higher rate of economic growth to catch up at least to one of her neighbours.

This requires cooperative moves from all parties which can be achieved by maintaining the commitment to the growth pact among all parties. It is necessary to design an incentive compatible mechanism by which it is in the best interest of each party to stick to such commitment.

Major focus of all parties has been to conduct a Constituent Assembly CA that would enshrine modern values, right and duties of each part of the nation and state, in the constitution of Nepalese people and open an unhindered path for rapid growth of the economy, uplifting the living standards of majority of people that would effectively eliminate illiteracy, expand education and health sectors and fulfil other basic needs to solve the problem of poverty for more than 25 million people in Nepal.

Gains from Bargaining and Shapley Values When parties enter into a coalition it should fulfil individual rationality, group rationality and coalition rationality.

These can be ascertained by the supper-additivity property of coalition where the maximisation of gain requires being a member of the coalition rather than playing alone. This can be explained using standard notations. Superadditivity condition implies that the value of the coalition of subset of players is more than value of the game only for one individual player. There are many ways the value of the game can be distributed among N different players.

At the core of the game each player gets at least as much from the coalition as from the individual action, this is equivalent to Pareto optimal allocation in a competitive equilibrium Sarf Some imputations are dominated by others; the core of the game is the strong criteria for dominant imputation.

Core satisfies coalition rationality.In game theorya cooperative game or coalitional game is a game with competition between groups of players "coalitions" due to the possibility of external enforcement of cooperative behavior e. Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing e. Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs.

It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria.

Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory the converse does not hold provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation.

While it would thus be possible to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately model the formal procedures available to the players during the strategic bargaining process, or the resulting model would be of too high complexity to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows the analysis of the game at large without having to make any assumption about bargaining powers.

A cooperative game is given by specifying a value for every coalition. The function describes how much collective payoff a set of players can gain by forming a coalition, and the game is sometimes called a value game or a profit game.

A game of this kind is known as a cost game. Although most cooperative game theory deals with profit games, all concepts can easily be translated to the cost setting. The Harsanyi dividend named after John Harsanyiwho used it to generalize the Shapley value in [5] identifies the surplus that is created by a coalition of players in a cooperative game.

To specify this surplus, the worth of this coalition is corrected by the surplus that is already created by subcoalitions. Harsanyi dividends are useful for analyzing both games and solution concepts, e. A cooperative game and its dual are in some sense equivalent, and they share many properties. For example, the core of a game and its dual are equal. For more details on cooperative game duality, see for instance Bilbao Subgames are useful because they allow us to apply solution concepts defined for the grand coalition on smaller coalitions.

Characteristic functions are often assumed to be superadditive Owenp. This means that the value of a union of disjoint coalitions is no less than the sum of the coalitions' separate values:. This follows from superadditivity. A coalitional game v is considered simple if payoffs are either 1 or 0, i. Equivalently, a simple game can be defined as a collection W of coalitions, where the members of W are called winning coalitions, and the others losing coalitions.

It is sometimes assumed that a simple game is nonempty or that it does not contain an empty set. However, in other areas of mathematics, simple games are also called hypergraphs or Boolean functions logic functions. A few relations among the above axioms have widely been recognized, such as the following e. More generally, a complete investigation of the relation among the four conventional axioms monotonicity, properness, strongness, and non-weaknessfiniteness, and algorithmic computability [9] has been made Kumabe and Mihara, [10]whose results are summarized in the Table "Existence of Simple Games" below.

The restrictions that various axioms for simple games impose on their Nakamura number were also studied extensively. Let G be a strategic non-cooperative game. Then, assuming that coalitions have the ability to enforce coordinated behaviour, there are several cooperative games associated with G.

These games are often referred to as representations of G. The two standard representations are: [13].

This assumption is not restrictive, because even if players split off and form smaller coalitions, we can apply solution concepts to the subgames defined by whatever coalitions actually form. Researchers have proposed different solution concepts based on different notions of fairness.

Some properties to look for in a solution concept include:.

An efficient payoff vector is called a pre-imputationand an individually rational pre-imputation is called an imputation. Most solution concepts are imputations. A stable set is a set of imputations that satisfies two properties:.Supplementary Appendix. An agent who privately knows his type good or bad seeks to be retained by a principal. A principal seeks to retain good agents.

Agents signal their type with some ambient noise, but can alter this noise, perhaps at some cost. A sender is about to come into possession of an object of heterogeneous quality. Prior to knowing that quality, she commits to a categorization. We apply these results to the design of educational grades.

Dedicated to Tapan Mitra — advisor, colleague and dear friend, whose sense of aesthetics, minimalism and rigor has been an inspiration to us. Tapan Mitra died on February 3, Every action profile therefore induces an interdependent utility system. A strategic situation is continuous if each such utility system is continuous.

If each utility system is bounded, with a unique payoff solution for every action profile, we call the strategic situation coherent, and if the same condition also applies to every subset of players, we call the situation sub-coherent.

A coherent, sub-coherent and continuous situation generates a standard normal form, referred to as a game of love and hate. Our central theorem states that every equilibrium of a game of love and hate is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities are restricted to flow only through payoffs there are no other constraints: they could be positive or negative, or of varying sign.

We further show that our coherence, sub-coherence and continuity requirements are tight. The stable set of von Neumann and Morgenstern can be extended to cover farsighted coalitional deviations, as proposed by Harsanyiand more recently reformulated by Ray and Vohra Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable, and easily verifiable, properties is unaffected by the imposition of this stringent maximality requirement.

This paper studies costly conflict over private and public goods. Oil is an example of the former, political power an example of the latter.International Economic Review, 59 4. ISSN We consider an intertemporal game-theoretic framework in which different coalitions interact repeatedly over time. Both the terms of trade and the endogenous cooperation structure arising in this setup are characterized, in a protocol-free manner, provided that just three natural conditions on the outcome are satisfied: C1 A coalition is formed with positive probability if, and only if, the shares obtained in this case by its members weakly exceed their respective share expectations.

C2 Each matched coalition distributes the entire surplus among its members. C3 Members of any coalition are treated symmetrically with respect to their share expectations when the surplus of this coalition is distributed. Our analysis primarily focuses on the limit scenario where the game ends each date with vanishing probability.

We show that, in this case, the cooperation structure and the shares are unique. In an application to trade networks, we show that, in a complete network, a unique price arises and agents specialize in either buying or selling. In an incomplete network, on the other hand, transactions occur, generally, at multiple prices and some agents become arbitrageurs that buy and sell at different prices.

Coalition bargaining in repeated games. Download kB Request a copy Preview. All rights reserved. Download kB Request a copy. Download kB Preview. Pure Connector.Author contributions: J. In society, power is often transferred to another person or group. A previous work studied the evolution of cooperation among robot players through a coalition formation game with a non-cooperative procedure of acceptance of an agency of another player. Motivated by this previous work, we conduct a laboratory experiment on finitely repeated three-person coalition formation games.

Human players with different strength according to the coalition payoffs can accept a transfer of power to another player, the agent, who then distributes the coalition payoffs. We find that the agencies method for coalition formation is quite successful in promoting efficiency.

## Cooperative game theory

However, the agent faces a tension between short-term incentives of not equally distributing the coalition payoff and the long-term concern to keep cooperation going. In a given round, the strong player in our experiment often resolves this tension approximately in line with the Shapley value and the nucleolus. One reason is that the voting procedure appears to induce a balance of power, independent of the individual player's strength: Selfish subjects tend to be voted out of their agency and are further disciplined by reciprocal behaviors.

The evolution of human altruism and cooperation is a puzzle. Unlike other animals, people frequently cooperate even absent of any material or reputational incentive to do so. In this paper we show how a voting procedure to transfer power to another person successfully promotes cooperation by balancing the tension between short-term incentives to defect and long-term incentives to keep cooperation going.

Our work is inspired by John Nash 1who theoretically studied the evolution of cooperation among robot players through acceptance of an agency of another player. The underlying idea is simple and important: Human subjects can transfer the power to an agency, who determines the final payoff distribution within the group.

The base games are finitely repeated for 40 rounds with the same three subjects, allowing cooperation and coordination to evolve. In our games non-cooperative game theory cannot organize behavior because it is basically consistent with any outcome. Thus, even the strategies of fully rational agents cannot be predicted by the theory. Yet understanding how cooperation is affected by decisions to transfer power to others requires theories that go beyond these approaches.

More specifically, our model specifies the coalition formation process in extensive form for more details see Methods and Fig. It consists of a coalition formation phase, and second phase in which the final agent distributes the coalition value. A given characteristic function specifies a value for all possible coalitions Table 1 shows the 10 three-person characteristic function games used in the experiment.

In phase 1 each player of a group of three can accept at most one other player as an agent to form a pair. In case nobody accepts, the phase is repeated until a pair is formed or a random break-up rule leads to zero payoffs for all. If one pair is formed, the accepting player becomes inactive and is represented by the accepted player who enters phase 2 together with the remaining player.

In case more than one pair is formed in phase 1, a random draw decides which pair is decisive for the next step. In phase 2, each of the two active players has to decide whether to accept the other active player. In case no one accepts, the stage is repeated until a player accepts or a random break-up rule selects the pair of stage 1 as the final coalition.

## Bargaining problem

In the latter case the accepted player of stage 1 divides the value of his two-person coalition. In case a player accepts in the second stage, the accepted player divides the three-person coalition value among the three players. If there are two accepted players in the second stage, a random draw selects which of the two players can divide the coalition value.

Characteristic functions, nucleolus, and Shapley values for the 10 games used in the experiment. Columns 5, 6, and 7 present the theoretical payoffs for players ABand Crespectively, according to nucleolus, and columns 8, 9, and 10 present those for the Shapley value in a one-shot cooperative game. These theoretical payoffs are always distributions of the grand coalition value.

Player A is the strong player in all games, because with him the highest two-person coalition payoffs can be achieved compared to a coalition without him. For a similar reason B is the second strongest player. In all theoretical cooperative solutions player A receives always the highest payoff, followed by player B. Flowchart of the experimental stage game: Each stage game within a round consists of two voting phases and a distribution phase.

The small black rectangles number the steps of the process. A rhomboid represents a switch with two exits for answers Yes and No to the question inside the rhomboid. As in rhomboids 4 and 10 the answer may be a realization of a random event.The two-person bargaining problem studies how two agents share a surplus that they can jointly generate.

It is in essence a payoff selection problem. In many cases, the surplus created by the two players can be shared in many ways, forcing the players to negotiate which division of payoffs to choose. There are two typical approaches to the bargaining problem. The normative approach studies how the surplus should be shared.

It formulates appealing axioms that the solution to a bargaining problem should satisfy. The positive approach answers the question how the surplus will be shared. Under the positive approach, the bargaining procedure is modeled in detail as a non-cooperative game. The Nash bargaining solution is the unique solution to a two-person bargaining problem that satisfies the axioms of scale invariance, symmetry, efficiency, and independence of irrelevant alternatives.

According to Walker, [1] Nash's bargaining solution was shown by John Harsanyi to be the same as Zeuthen 's solution [2] of the bargaining problem. The Nash bargaining game is a simple two-player game used to model bargaining interactions. In the Nash bargaining game, two players demand a portion of some good usually some amount of money. If the total amount requested by the players is less than that available, both players get their request.

If their total request is greater than that available, neither player gets their request. Nash presents a non-cooperative demand game with two players who are uncertain about which payoff pairs are feasible.

### Coalitional Bargaining in Networks

In the limit as the uncertainty vanishes, equilibrium payoffs converge to those predicted by the Nash bargaining solution. Rubinstein also modelled bargaining as a non-cooperative game in which two players negotiate on the division of a surplus known as the alternating offers bargaining game.

The division of the surplus in the unique subgame perfect equilibrium depends upon how strongly players prefer current over future payoffs.

In the limit as players become perfectly patient, the equilibrium division converges to the Nash bargaining solution. For a comprehensive discussion of the Nash bargaining solution and the huge literature on the theory and application of bargaining - including a discussion of the classic Rubinstein bargaining model - see Abhinay Muthoo 's book Bargaining Theory and Application.

The feasible agreements typically include all possible joint actions, leading to a feasibility set that includes all possible payoffs.

Often, the feasible set is restricted to include only payoffs that have a possibility of being better than the disagreement point for the agents that are bargaining.

This could be some focal equilibrium that both players could expect to play. This point directly affects the bargaining solution, however, so it stands to reason that each player should attempt to choose his disagreement point in order to maximize his bargaining position. Towards this objective, it is often advantageous to increase one's own disagreement payoff while harming the opponent's disagreement payoff hence the interpretation of the disagreement as a threat.

If threats are viewed as actions, then one can construct a separate game wherein each player chooses a threat and receives a payoff according to the outcome of bargaining.

It is known as Nash's variable threat game. Strategies are represented in the Nash demand game by a pair xy. There are many Nash equilibria in the Nash demand game. If either player increases their demand, both players receive nothing. If either reduces their demand they will receive less than if they had demanded x or y.

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