Non-transferable Utility Research Articles

Matching under Non-transferable Utility: Applications

Matching under Non-transferable Utility: Applications

Matching under Non-transferable Utility: Theory

Matching under Non-transferable Utility: Theory

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.

The equal split-off set for NTU-games

This paper introduces and studies the equal split-off set for cooperative games with nontransferable utility. We illustrate the new solution for the well-known Roth-Shafer examples and present two axiomatic characterizations based on different consistency properties on the class of exact partition games, i.e. the class of games where it intersects the core.

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.

Generalizing the constrained equal awards rule

This paper studies axiomatic characterizations of the constrained equal awards rule for bankruptcy problems. We show that many results apply in a much more general context than for which they are originally formulated. In particular, we generalize several axiomatic characterizations based on symmetry, sustainability, and consistency to the domain of bankruptcy problems with nontransferable utility.

Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility

Endogenous Duration of Long-term Agreements in Cooperative Dynamic Games with Nontransferable Utility

A random arrival rule for NTU-bankruptcy problems

This paper introduces and studies a random arrival rule for bankruptcy problems with nontransferable utility. This bankruptcy rule generalizes the random arrival rule for bankruptcy problems with transferable utility which assigns the unique efficient allocation proportional to the sum of marginal vectors. We provide two axiomatic characterizations based on symmetry and monotonicity, respectively.

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.

The Replicated Core under Multi-Choice Non-Transferable- Utility Situations: Converse Reduction Axiomatic Enlargements

Since the replicated core counters the (inferior) converse reduction axiom under multi-choice non-transferable-utility (NTU) situations, two converse reduction axiomatic enlargements of the replicated core are generated. These two enlargements are the smallest (inferior) converse reduction axiomatic solutions that contain the replicated core. Finally, relative axiomatic results are also provided.

On the revealed preference analysis of stable aggregate matchings

Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable and nontransferable utility and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalizable. For matchings that are not rationalizable, we provide a simple greedy algorithm that computes the minimum number of matches that need to be removed to obtain a rationalizable matching. We also show that the related problem of finding the minimum number of types that we need to remove in order to obtain a rationalizable matching is NP‐complete.

Plenty of Fish in the Sea: Divorce Choice and the Quality of Singles

In the literature of marriage, divorce choices are usually assumed to not affect the distribution of types in the pool of singles. The scope of the present paper is to overcome this assumption. We analyse divorce choices when separation decision influences the distribution of singles and, thus, their expected quality. We consider a three-period model where heterogeneous individuals may unilaterally experience divorce and return to the marriage market. The choices of individuals are based on the change in the distribution of singles and the cost of waiting and divorcing, taking into consideration the individual’s eligibility in the marriage market. There are two main findings: Firstly, positive assortative matching dissolves with divorce for some intermediate types. Therefore, the endogenous positive assortative matching that usually emerges in models with nontransferable utility is weakened when matches can dissolve. Secondly, the existence of ranges where divorce emerges among individuals with positive assortative matching implies the existence of two disconnected classes of types. If matchings in the first period were to occur between individuals of different classes, such matches would be dissolved later.

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.

Stability in sequential matching with incomplete information

I study a two-period matching model where one side of the market (e.g. workers) have an option to invest and delay matching in the first period. Investment increases each agent's matching surplus in the second period, by a magnitude of the worker's investment ability in the match pair. Assuming each worker's investment ability is her private information that unfolds in the second period, I define a notion of sequential stability, and show that the set of sequentially stable outcomes is a superset of the complete information stable outcomes. Moreover, with transferable utility, as long as the cost of delay coincides on the same side of the market, efficient investment occurs in any sequentially stable outcome. When every agent shares the same cost of delay, efficient investment also occurs in any sequentially stable outcome with non-transferable utility. My analysis suggests that efficient investment is a robust prediction in sequential matching markets.

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.

Consumer Flexibility Aggregation Using Partition Function Games With Non-Transferable Utility

This paper explores the aggregation of electricity consumers flexibility. A novel coalitional game theory model for partition function games with non-transferable utility is proposed. This model is used to formalize a game in which electricity consumers find coalitions among themselves in order to trade their consumption flexibility in the electricity market. Utility functions are defined to enable measuring the players preferences. Two case studies are presented, including a simple illustrative case, which assesses and explains the model in detail; and a large-scale scenario based on real data, comprising more than 20,000 consumers. Results show that the proposed model is able to reach solutions that are more suitable for the consumers when compared to the solutions achieved by traditional aggregation techniques in power and energy systems, such as clustering-based methodologies. The solutions found by the proposed model consider the perspectives from all players involved in the game and thus are able to reflect the rational behaviour of the involved players, rather than imposing an aggregation solution that is only beneficial from the perspective of the aggregator.

A multi-objective optimisation model for train scheduling in an open-access railway market

ABSTRACT Liberalised railway markets bring into play the economic interactions amongst three dominant interest groups: passengers as system users; public entities providing the track; and private firms operating the trains. Problems that arise are multi-criteria with multi-decision-makers who may be in conflict. Our approach to this problem is similar to that of a cooperative game-theoretic non-transferable utility (NTU) to reach Pareto optimal resolutions in which the aspirations of all players are taken into account. The data are collected from the Istanbul-Ankara high-speed railway via a stated preference survey. A multi-agent system (MAS) is developed via GOLang, a programming language where the agents negotiate and interact with others based on a set of parameters such as ticket price setting and resource allocation. The results show better timetabling for trains and how to achieve higher compensation rates for the infrastructure provider by collecting higher amounts of track access charges from an optimised allocation of resources.

Characterizing NTU-bankruptcy rules using bargaining axioms

This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility, by using properties from bargaining theory in order to characterize bankruptcy rules. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule, using properties which concern changes in the estate or in the claims.

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.