Non-transferable Utility Games Research Articles

Average monotonic cooperative games with nontransferable utility

A non-negative transferable utility (TU) game is average monotonic if there exists a non-negative vector according to which the relative worth is not decreasing when enlarging the coalition. We generalize this definition to the nontransferable utility (NTU) case. It is shown that an average monotonic NTU game shares several properties with an average monotonic TU game. In particular it has a special core element and there exists a population monotonic allocation scheme. We show that an NTU bankruptcy game is average monotonic with respect to the claims vector.

On Balanced Host Games: A Sufficient Condition for Non-Emptiness of the Core

Non-transferable utility (NTU) games arise from many economic situations. A classic example is the exchange economy. By pooling and redistributing their initial endowments, coalitions can achieve certain distributions of gains (utilities) that make up the coalition’s feasible set. This paper studies a new class of NTU games called host games. A host game is an agent-parametrized family of NTU games, and an NTU game is associated with any agent (called the host in that case). We provide an adequate presumption for the existence of an allocation that is part of the host game’s core.

Cooperative solutions for TU and NTU stochastic game-theoretical approach

The player's payoff in stochastic games is a stochastic variable. In most studies, predicted payout is referred to as a payoff, implying that the players are risk averse. However, there may be risk-averse players that consider "risk" while calculating their stochastic payoffs. We offer a model of stochastic games using mean-variance reward functions, which are the sum of expectation and standard deviation multiplied by a coefficient indicating a player's risk aversion. By adopting a maxmin technique to define the characteristic function, we may create a cooperative version of a stochastic game with mean-variance preferences. This paper contains an analysis of a cooperative solution concept of stochastic games for both TU (transferable utility) and NTU (non-transferable utility) games. We proposed a cooperative game solution method of extension of two-person zero sum strategic game to n-agent stochastic stage game using both Shapley and Banzhaf index functions. Results are proved for both discounted and undiscounted payoff situations. Existing models of discrete-time stochastic games and ways to finding cooperative solutions in these games are extended in this study.

Answers set programs for non-transferable utility games: Expressiveness, complexity and applications

Coalitional games are mathematical models suited to study payoff distribution problems in cooperative scenarios. In abstract terms, a coalitional game can be specified by explicitly listing all possible—in fact, exponentially many—coalitions with their associated distributions. This naïve representation, however, quickly becomes infeasible over games involving many agents, thereby calling for suitable compact representations, that is, encoding mechanisms that (on some specific classes of games of interest) take an amount of space that grows polynomially with the number of agents. To date, a plethora of compact encodings have been already introduced and analyzed from the algorithm and computational viewpoints. Despite their specific technical differences, these encodings typically share the assumption that the utility associated with a coalition can be freely transferred among agents. Indeed, designing encoding mechanisms for the non-transferable utility (NTU) setting is a research issue that has been largely unexplored so far.The paper addresses this issue by proposing a compact encoding for representing and reasoning about the outcomes of NTU coalitional games founding on answer set programming. By exploiting the expressiveness of this well-known knowledge representation formalism, it is shown that the proposed representation can succinctly encode several games of interest within a wide range of application domains. Computational issues arising in the setting have been studied too, by addressing questions related to certain payoff distributions enjoying desirable stability properties. Eventually, a prototype system supporting the proposed framework has been implemented by leveraging a state-of-the-art answer set engine, and results of a thorough experimental activity conducted on top of it have been discussed.

The bargaining set and coalition formation

We study solution concepts for nontransferable utility games according to which the coalition structure and the payoff allocations are simultaneously determined. The steady bargaining set is a refinement of the Zhou bargaining set, which is included in the Mas‐Colell bargaining set. We prove the nonemptiness and partial efficiency of the steady bargaining set for at least one coalition structure under the restrictive non‐crossing condition. Without this condition, the Zhou bargaining set may be empty and the Mas‐Colell bargaining set is nonempty but may not be efficient.

A cooperative game based mechanism for autonomous organization and ubiquitous connectivity in VANETs

Vehicular communications in Vehicular Ad-hoc NETworks (VANETs) play an interesting role in improving traffic flow on the roads. In such wireless networks, the vehicles cooperate with each other or with the roadside infrastructure to disseminate the data. In this paper, we introduce a mechanism based on coalitional game theory to study the cooperative transmission in VANETs. Each vehicle tries to access the Internet via gateways that can be either fixed or mobile. However, these gateways help the vehicles to access the Internet by cooperatively relaying the vehicles’ messages. Thus, two notions to indicate the availability of transmission between vehicles and gateways are introduced. These notions are chosen to deal with the highly dynamic topology in VANETs, namely the notion of an encounter and the notion of a link’s predicted lifetime. The problem is modelled as a non-transferable utility game. Then, an algorithm is proposed to dynamically form coalitions among the vehicles. Moreover, a probability of being active is set in terms of speed of the received vehicle. To evaluate the proposed solution, two scenarios are used: fixed gateways scenario and mobile gateways scenario. The numerical results show that the scenario of mobile gateways is more effective in terms of stimulating vehicles to regroup into coalitions. Hence, this helps the vehicles to access the Internet.

On the values of Bayesian cooperative games with sidepayments

In this paper, we study the solution concept of value in transferable utility (TU) games with asymmetric information. In our model contingent contracts are required to be incentive compatible, and thus utility might not be not fully transferable. Our approach differs from the standard methodology of TU games with complete information, which summarizes the cooperative possibilities through the characteristic function. Instead, we consider a model in which monetary transfers are modeled as additional sidepayments in a non-transferable utility (NTU) game. Our main result states that [18] generalization of the Shapley NTU value and Salamanca (2020) extension of the Harsanyi NTU value are interim utility equivalent in our model with sidepayments. As a consequence of this result, we obtain a generalization of the Shapley TU value to games with incomplete information. Its formula, however, cannot be described by a simple closed form expression as in the case of complete information.

A procedural egalitarian solution for NTU-games

This paper introduces and analyzes a procedural egalitarian solution for nontransferable utility games. This concept is based on an egalitarian procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which the new solution prescribes a core element and derive a direct expression on the class of bargaining games and the class of bankruptcy games.

Cooperative games with nontransferable utility on antimatroids

ABSTRACTThis paper introduces a new family of nontransferable utility (NTU) games with partial cooperation. Games with transferable utility (TU) restricted by antimatroids were studied since 2004. Antimatroids are known combinatorial structures which are interpreted in games as dependency situations among a group of agents, and they generalize several other hierarchical structures studied in the literature. Now we define projected NTU games over antimatroids following the same idea. We have needed to build a new theory about projections between two coalitions. In this case, an outcome is feasible for a coalition if and only if its projection is feasible in the NTU game. This paper studies several properties of the projected games and the relations between these games and the original game for some interesting cases: TU games, hyperplane games and bargaining problems.

The Harsanyi value for nontransferable utility games with restricted cooperation

A nontransferable utility (NTU) game assigns a set of feasible pay-off vectors to each coalition. In this article, we study NTU games in situations in which there are restrictions on coalition formation. These restrictions will be modelled through interior structures, which extend some of the structures considered in the literature on transferable utility games for modelling restricted cooperation, such as permission structures or antimatroids. The Harsanyi value for NTU games is extended to the set of NTU games with interior structure.

Data Offloading in Mobile Edge Computing: A Coalition and Pricing Based Approach

Mobile edge computing (MEC) that affords service to the vicinity of mobile devices (MDs) has become a key technology for future network. Offloading big data to the MEC server for preprocessing is an attractive approach of MDs. In this paper, we investigate data offloading from MDs to MEC servers, and a coalitional game-based pricing scheme is proposed. We apply coalitions to arrange data offloading of MDs as well as depict the offloading relationship between MDs and MEC servers. Furthermore, pricing is utilized as the stimuli for the offloading. In the proposed scheme, a scheduled MD in a coalition chooses an MEC server within the same coalition for offloading, and pays the selected MEC server for the MEC service. By analyzing the formulated coalitional non-transferable utility game, theoretical properties are derived and sufficient conditions for the core existence are given. Finally, the utility performances of the proposed scheme are demonstrated by numerical results.

Nontransferable utility games with fuzzy coalition restrictions

A value for nontransferable utility (NTU) games with fuzzy coalition restrictions is introduced and characterized. In a similar way as the Shapley value for transferable utility (TU) games has been extended in the literature to study games with restricted cooperation, we extend the Shapley NTU value to deal with NTU games in situations in which there are fuzzy dependency relationships among the players.

Egalitarianism in Nontransferable Utility Games

This paper studies egalitarianism in the context of nontransferable utility games by introducing and analyzing the egalitarian value. This new solution concept is based on an egalitarian negotiation procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which it leads to a core element and discuss the egalitarian value for the well-known Roth-Shafer examples. Moreover, we characterize the new value on the class of bankruptcy games and bargaining games.

An equilibrium cooperative optimization solution for two-person non-transferable utility games

An equilibrium cooperative optimization solution for two-person non-transferable utility games

Characterizations of the core of TU and NTU games with communication structures

It is well-known that the core on several domains of cooperative transferable utility (TU) and nontransferable utility (NTU) games is characterized by various combinations of axioms containing some versions of the reduced game property, of its converse, or of the reconfirmation property with respect to the Davis–Maschler reduced game. We show that these characterizations are still valid for games with communication structures a la Myerson when using the notion of the reduced communication structure that establishes a new link between two inside players if they can communicate via outside players. Thus, it is shown that, if communication structures are present, the core may still be characterized on balanced TU games, on totally balanced TU games, on NTU games with a nonempty core, on the domains of all TU or NTU games, and on several other interesting domains of TU and NTU games. As a byproduct we construct, for any NTU game with communication structure, a certain classical NTU game with the same core that may be regarded as its Myerson restricted NTU game.

Unification of Oligopolistic Markets for a Homogeneous Good in the Presence of an Antitrust Commission

A basic framework is provided to explain the integration process experienced by oligopolistic markets serving a homogeneous good in different countries. Over the past few decades, such processes have been observed, for instance, in some European markets – in particular, in the energy sector. The idiosyncratic element here is the introduction of an exogenously given antitrust commission that supervises competition in the market and has the authority to fine firms for anticompetitive behavior. We model the unification decision as a simple cooperative non-transferable utility game. We find that the creation of an antitrust commission plays a major role in providing the necessary incentives for market unification. In particular, the commission is able to induce unification of all markets via appropriate choice of antitrust policy. This stands in stark contrast to the benchmark scenario in which the antitrust commission is absent – here, market unification never occurs. We propose the Iberian Electricity Market (MIBEL) as a case study.

Competitive outcomes and the inner core of NTU market games

We consider the inner core as a solution concept for cooperative games with non-transferable utility (NTU) and its relationship to payoffs of competitive equilibria of markets that are induced by NTU games. An NTU game is an NTU market game if there exists a market such that the set of utility allocations a coalition can achieve in the market coincides with the set of utility allocations the coalition can achieve in the game. In this paper, we introduce a new construction of a market based on a closed subset of the inner core which satisfies a strict positive separability. We show that the constructed market represents the NTU game and, further, has the given closed set as the set of payoff vectors of competitive equilibria. It turns out that this market is not uniquely determined, and thus, we obtain a class of markets. Our results generalize those relating to competitive outcomes of NTU market games in the literature.

On the Core of Games with Communication Structures

It is well-known that the core on several domains of cooperative transferable utility (TU) and nontransferable utility (NTU) games is characterized by various combinations of axioms containing some versions of the reduced game property, of its converse, or of the reconrmation property with respect to the Davis-Maschler reduced game. We show that these characterizations are still valid for games with communication structures a la Myerson when using the notion of the reduced communication structure that establishes a new link between two inside players if they can communicate via outside players. Thus, it is shown that, if communication structures are present, the core may still be characterized on balanced TU games, on totally balanced TU games, on NTU games with a nonempty core, on the domains of all TU or NTU games, and on several other interesting domains of TU and NTU games. As a byproduct we construct, for any NTU game with communication structure, a certain classical NTU game with the same core that may be regarded as its Myerson restricted NTU game.

Resource Allocation for M2M Communication in Heterogeneous Network: Coalitional Game Theory Approach

The heterogeneous cellular network (HCN) is a promising technology to handle the rising number of devices due to their universal presence. This rising popularity HCN based Machine-to-Machine (M2M) communications is opening new opportunities and also bringing forth new system design issues. However, the main challenge of M2M communication is the possibility of huge traffic and significant difference in the nature of M2M traffic than the current commercial traffic for which current cellular network is designed and optimized. In this article, we investigate the uplink resource allocation problem of M2M devices (MDs) in the multiple Femto base station's coverage. We first model the uplink power and sub-carrier allocation in femtocells independently; Based on the cooperative game resource allocation among MDs is analyzed through non-transferable utility game to enhance the data rate performance with minimum utilization of power. Simulation results show that the resource allocation model based on cooperative game is able to provide a fair distribution of data rate compared with non-cooperative and greedy type of MDs.

Book Reviews

Omer Edhan of University of Manchester reviews, “Value Solutions in Cooperative Games” by Roger A. McCain. The Econlit abstract of this book begins: “Presents new concepts for cooperative game theory, with a particular focus on solutions that determine the distribution of a coalitional surplus among the members of the coalition. Discusses value solutions for superadditive transferable utility games in coalition function form; Zeuthen–Nash bargaining; nontransferable utility games and games in partition function form; a Shapley value algorithm for games in partition function form; extension of the nucleolus to nontransferable utility games in partition function form; a core imputation with variable bargaining power; bargaining power biform games; intertemporal cooperative games—a sketch of a theory; and a theory of enterprise. McCain is at Drexel University.”