Majority bargaining for resource division

We address the problem of how a set of agents can decide to share a resource, represented as a unit-sized pie. The pie can be generated by the entire set but also by some of its subsets. We investigate a finite horizon non-cooperative bargaining game, in which the players take it in turns to make proposals on how the resource should for this purpose be allocated, and the other players vote on whether or not to accept the allocation. Voting is modelled as a Bayesian weighted voting game with uncertainty about the players’ weights. The agenda, (i.e., the order in which the players are called to make offers), is defined exogenously. We focus on impatient players with heterogeneous discount factors. In the case of a conflict, (i.e., no agreement by the deadline), no player receives anything. We provide a Bayesian subgame perfect equilibrium for the bargaining game and conduct an ex-ante analysis of the resulting outcome. We show that the equilibrium is unique, computable in polynomial time, results in an instant Pareto optimal outcome, and, under certain conditions provides a foundation for the core and also the nucleolus of the Bayesian voting game. In addition, our analysis leads to insights on how an individual’s bargained share is in- fluenced by his position on the agenda. Finally, we show that, if the conflict point of the bargaining game changes, then the problem of determining the non-cooperative equilibrium becomes NP-hard even under the perfect information assumption. Our research also reveals how this change in conflict point impacts on the above mentioned results

Multilateral bargaining for resource division

We address the problem of how a group of agents can decide to share a resource, represented as a unit-sized pie. We investigate a finite horizon non-cooperative bargaining game, in which the players take it in turns to make proposals on how the resource should be allocated, and the other players vote on whether or not to accept the allocation. Voting is modelled as a Bayesian weighted voting game with uncertainty about the players’ weights. The agenda, (i.e., the order in which the players are called to make offers), is defined exogenously. We focus on impatient players with heterogeneous discount factors. In the case of a conflict, (i.e., no agreement by the deadline), all the players get nothing. We provide a Bayesian subgame perfect equilibrium for the bargaining game and conduct an ex-ante analysis of the resulting outcome. We show that, the equilibrium is unique, computable in polynomial time, results in an instant Pareto optimal agreement, and, under certain conditions provides a foundation for the core of the Bayesian voting game. Our analysis also leads to insights on how an individual’s bargained share is in- fluenced by his position on the agenda. Finally, we show that, if the conflict point of the bargaining game changes, then the problem of determining a non-cooperative equilibrium becomes NP-hard even under the perfect information assumption

Power and welfare in bargaining for coalition structure formation

We investigate a noncooperative bargaining game for partitioning n agents into non-overlapping coalitions. The game has n time periods during which the players are called according to an exogenous agenda to propose offers. With probability δ, the game ends during any time period t< n. If it does, the first t players on the agenda get a chance to propose but the others do not. Thus, δ is a measure of the degree of democracy within the game (ranging from democracy for δ= 0 , through increasing levels of authoritarianism as δ approaches 1, to dictatorship for δ= 1). We determine the subgame perfect equilibrium (SPE) and study how a player’s position on the agenda affects his bargaining power. We analyze the relation between the distribution of power of individual players, the level of democracy, and the welfare efficiency of the game. We find that purely democratic games are welfare inefficient and that introducing a degree of authoritarianism into the game makes the distribution of power more equitable and also maximizes welfare. These results remain invariant under two types of player preferences: one where each player’s preference is a total order on the space of possible coalition structures and the other where each player either likes or dislikes a coalition structure. Finally, we show that the SPE partition may or may not be core stable

Bargaining for coalition structure formation

Many multiagent settings require a collection of agents to partition themselves into coalitions. In such cases, the agents may have conflicting preferences over the possible coalition structures that may form. We investigate a noncooperative bargaining game to allow the agents to resolve such conflicts and partition themselves into non-overlapping coalitions. The game has a finite horizon and is played over discrete time periods. The bargaining agenda is de- fined exogenously. An important element of the game is a parameter 0 ≤ δ ≤ 1 that represents the probability that bargaining ends in a given round. Thus, δ is a measure of the degree of democracy (ranging from democracy for δ = 0, through increasing levels of authoritarianism as δ approaches 1, to dictatorship for δ = 1). For this game, we focus on the question of how a player’s position on the agenda affects his power. We also analyse the relation between the distribution of the power of individual players, the level of democracy, and the welfare efficiency of the game. Surprisingly, we find that purely democratic games are welfare inefficient due to an uneven distribution of power among the individual players. Interestingly, introducing a degree of authoritarianism into the game makes the distribution of power more equitable and maximizes welfare

Optimal coalition structures for probabilistically monotone partition function games

For cooperative games with externalities, the problem of optimally partitioning a set of players into disjoint exhaustive coalitions is called coalition structure generation, and is a fundamental computational problem in multi-agent systems. Coalition structure generation is, in general, computationally hard and a large body of work has therefore investigated the development of efficient solutions for this problem. However, the existing methods are mostly limited to deterministic environments. In this paper, we focus attention on uncertain environments. Specifically, we define probabilistically monotone partition function games, a subclass of the well-known partition function games in which we introduce uncertainty. We provide a constructive proof that an exact optimum can be found using a greedy approach, present an algorithm for finding an optimum, and analyze its time complexity.</p

The negotiation game

In this paper, the authors consider some of the main ideas underpinning attempts to build automated negotiators--computer programs that can effectively negotiate on our behalf. If we want to build programs that will negotiate on our behalf in some domain, then we must first define the negotiation domain and the negotiation protocol. Defining the negotiation domain simply means identifying the space of possible agreements that could be acceptable in practice. The negotiation protocol then defines the rules under which negotiation will proceed, including a rule that determines when agreement has been reached, and what will happen if the participants fail to reach agreement. One important insight is that we can view negotiation as a game, in the sense of game theory: for any given negotiation domain and protocol, negotiating agents have available to them a range of different negotiation strategies, which will result in different outcomes, and hence different benefits to them. An agent will desire to choose a negotiation strategy that will yield the best outcome for itself, but must take into account that other agents will be trying to do the same