Non-cooperative Bargaining Game Research Articles

Recursive and bargaining values

We introduce two families of values for TU-games: the recursive and bargaining values. Bargaining values are obtained as the equilibrium payoffs of the symmetric non-cooperative bargaining game proposed by Hart and Mas-Colell (1996). We show that bargaining values have a recursive structure in their definition, and we call this property recursiveness. All efficient, linear, and symmetric values that satisfy recursiveness are called recursive values. We generalize the notions of potential, and balanced contributions property, to characterize the family of recursive values. Finally, we show that if a time discount factor is considered in the bargaining model, every bargaining value has its corresponding discounted bargaining value.

Optimal recommendation in two-player bargaining games

This paper extends the traditional two-player noncooperative bargaining game by adding a recommendation stage before the regular bargaining stage. At the recommendation stage, a coordinator recommends a feasible payoff pair to the players. If both players accept the recommendation, the game ends and the recommendation is enforced. Otherwise, the game enters the bargaining stage, where each player is picked as the proposer of any bargaining round according to an exogenous probability characterizing their relative bargaining power, and both players receive their respective reservation payoffs with a certain risk of breakdown if they fail to reach an agreement in this round. We characterize the unique subgame perfect equilibrium outcome of this extended game. The equilibrium recommendation, which will be accepted by both players, is optimal for the coordinator among all acceptable recommendations. A player’s payoff in optimal recommendation increases with her bargaining power. As the risk of breakdown vanishes, the optimal recommendation converges to an asymmetric Nash bargaining solution parameterized by the probability at the bargaining stage.

A noncooperative bargaining game with endogenous protocol and partial breakdown

In this paper, we present a noncooperative sequential bargaining game with transferable utility. Instead of assuming exogenous protocol or random-proposer recognition, we provide a mechanism in which the protocol is generated endogenously. Besides, a partial breakdown probability is considered rather than a discount factor when the proposal is rejected by some player. We show that for each partial breakdown probability, stationary subgame perfect equilibria exist if the characteristic function game is totally balanced. Moreover, the outcomes of stationary subgame perfect equilibria in our model coincide with the core allocations.

A sequential bargaining protocol for land rental arrangements

We consider land rental between a single tenant and several lessors. The tenant should negotiate sequentially with each lessor for the available land. In each stage, we apply the Nash bargaining solution, as a short-cut to solving non-cooperative bargaining games. Our results imply that, when all land is necessary, a uniform price per unit is more favorable for the tenant than a lessor-dependent price. Furthermore, a lessor is better off with a lessor-dependent price only when negotiating first. For the tenant, lessors’ merging is relevant with lessor-dependent price but not with uniform price.

Nash Bargaining-Based Economic Analysis of Opportunistic Cognitive Cellular Networks

We analyse a cognitive cellular network comprising of a primary and a secondary network operator (PNO and SNO). The SNO implements distributed detection to opportunistically access the licensed band. In return, the PNO requests the SNO to pay a remuneration. The PNO judiciously balances between the revenue gained from its subscribers and the payment earned from the SNO. On the other hand, the SNO must earn a positive utility to maintain its infrastructure. Consequently, a two-person non-cooperative bargaining game is formulated where the operators agree upon the value of the following factors: base station activity probabilites and the payment from the SNO. The PNO is aware of detection and false-alarm probabilities of spectrum sensing by the SNO and hence can infer how the interference created by missed detection degrades its capacity. We establish that our formulated game has a unique Nash solution. For linear demands, we derive an approximate closed-form solution. Numerical analysis reveals several insightful results. For example, we exhibit that, if the user number of the SNO lies below a certain threshold, the cognitive network appears to be economically unsustainable. We also show the functional dependence of the bargaining outcome on various system parameters.

Bilateral bargaining with endogenous status quo

We consider a non-cooperative bargaining game where in each round, if a proposal is rejected, with a probability, the allocation implemented in the previous round is implemented as a status quo and the game proceeds to the next round, and with the complementary probability, no allocations are implemented and the negotiations break down. We show that there exists a unique stationary subgame perfect equilibrium such that in any round, a proposer offers a proposal such that the responder is indifferent between accepting and rejecting it and an agreement is achieved. If the probability of breakdown is close to zero, the sequence of equilibrium allocations evolves from the initial status quo to an allocation near the equilibrium allocation of the Rubinstein bargaining game over time. The effect of the initial status quo on the equilibrium allocations vanishes over time.

On gamesmen and fair men: explaining fairness in non-cooperative bargaining games.

Experiments on bargaining games have repeatedly shown that subjects fail to use backward induction, and that they only rarely make demands in accordance with the subgame perfect equilibrium. In a recent paper, we proposed an alternative model, termed ‘economic harmony’ in which we modified the individual's utility by defining it as a function of the ratio between the actual and aspired pay-offs. We also abandoned the notion of equilibrium, in favour of a new notion of ‘harmony’, defined as the intersection of strategies, at which all players are equally satisfied. We showed that the proposed model yields excellent predictions of offers in the ultimatum game, and requests in the sequential common pool resource dilemma game. Strikingly, the predicted demand in the ultimatum game is equal to the famous Golden Ratio (approx. 0.62 of the entire pie). The same prediction was recently derived independently by Schuster (Schuster 2017. Sci. Rep. 7, 5642). In this paper, we extend the solution to bargaining games with alternating offers. We show that the derived solution predicts the opening demands reported in several experiments, on games with equal and unequal discount factors and game horizons. Our solution also predicts several unexplained findings, including the puzzling ‘disadvantageous counter-offers’, and the insensitivity of opening demands to variations in the players' discount factors, and game horizon. Strikingly, we find that the predicted opening demand in the alternating offers game is also equal to the Golden Ratio.

Rent-seeking and surplus destruction in unanimity bargaining

In non-cooperative bargaining games in the tradition of Rubinstein, the proposer's bargaining power stems from the prospect of a delay in case of disagreement. Since players are impatient, this delay is costly for everyone. We consider a unanimity bargaining game in which the proposer can strategically choose the length of this delay. We assume that the size of the surplus depends endogenously on the chosen length of the prospective delay. Intuitively, the proposer faces the following trade-off: The more he exploits his proposer power, the smaller is the surplus that can be divided. One interpretation is that aggressive bargaining tactics hurt the fruitful cooperation among players, and thus the surplus. We characterize stationary equilibrium strategies and payoffs, and obtain sharp predictions on the extent of surplus destruction, the size of the social loss, and the surplus allocation.

A Non-cooperative Mechanism Yielding the Nucleolus of Airport Problems

A non-cooperative approach is employed to solve the problem of allocating the total cost of building and maintaining an airport runway among its users. More precisely, it is proposed a non-cooperative bargaining game with a unique subgame perfect equilibrium (SPE) outcome, and it is shown that the SPE outcome payoffs coincide with those prescribed by the nucleolus of the corresponding airport cooperative game.

Decision sciences in the management of water resources: multi-criteria methods and game theory applied to the field of sanitation

Due to the complexity of some managerial problems, especially those related to sanitation, academic studies have shown the need to use appropriate methods to assist in this type of decision. Within this context, this research aimed to provide a review of the literature from the field of decision sciences to the field of water resource management. It was identified in this study that the use of multi-criteria methods, including Analytical Hierarchy Process, Measuring Attractiveness by a Categorical based Evaluation Technique, Multiattribute Utility Theory, Elimination et Choice Traduisant la Realité, Preference Ranking Organization Method for Enrichment Evaluations, Technique for Order Preference by Similarity to Ideal Solution, and game theory, including cooperative and non-cooperative bargaining games, are useful for creation and comparison of scenarios, reducing the time needed to reach a solution for complex problems involving a large number of criteria and agents. It also demonstrated the benefits of creating greater transparency in the decision-making process, thus increasing the potential for a solution acceptable to all the parties involved. Although still little explored, discussions of sanitation problems can and should be enhanced with the use of techniques and methods of decision sciences, and multi-criteria and game theory techniques are particularly suitable for this task.

Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games

We propose a solution concept for a class of extensive form games with ambiguity. Specifically we consider multi-stage games. Players have CEU preferences. The associated ambiguous beliefs are revised by Generalized Bayesian Updating. We assume individuals take account of possible changes in their preferences by using consistent planning. We show that if there is ambiguity in the centipede game it is possible to sustain `cooperation' for many periods as part of a consistent-planning equilibrium under ambiguity. In a non-cooperative bargaining game we show that ambiguity may be a cause of delay in bargaining.

An information congestion control scheme in the Internet of Vehicles: A bargaining game approach

In VANETs (Vehicular Ad Hoc Networks), the information exchange plays an important role for context awareness. However, at intersections, a channel congestion is likely occurring if no control scheme is applied for the exchange especially when the vehicle density is high. To solve this problem, a congestion control scheme is proposed based on the non-cooperative bargaining game. First, vehicles approaching intersections are divided into clusters. By introducing a simple channel-load estimation scheme, our bargaining game is presented by which the cluster leaders could negotiate an optimal combination of the transmitting power and packet generation rate for their members. When the Nash Equilibrium of our game is reached, the utility of each player will be maximized without making the channel congested. Numerical results show that our scheme could alleviate the possible packets collisions thus reducing the average experienced delay and increasing the packets delivery ratio on the receiver side.

Do Workers Negotiate Collectively or Separately? An Application of a Coalitional Bargaining Game with Externalities

This study proposes a non-cooperative coalitional bargaining game model to analyse wage negotiations between one employer and two workers. Here, randomly selected workers choose whether to negotiate their wage contracts together or separately, considering wage contract externalities. We show that if the two workers are sufficiently complementary or if externalities are more positive, there exists a grand-coalition SSPE of the bargaining game for any discount factor. However, if the two workers are sufficiently substitutable, there is no grand-coalition SSPE for any discount factor. In addition, we provide a sufficient condition for an SSPE to exist, in which each worker selects separate negotiations with the employer.

Destroying Surplus and Buying Time in Unanimity Bargaining

In non-cooperative bargaining games in the tradition of Rubinstein, the proposer derives bargaining power from the prospect of a costly delay which would follow the rejection of a proposal. We consider a unanimity bargaining game in which the proposer can strategically choose to prolong this delay. Prolonging the delay increases the proposer's bargaining power, but is assumed to come at a cost and thus cause an inefficiency. We use an appropriate refinement of stationary subgame-perfect equilibrium as the solution concept. We characterize equilibrium strategies and payoffs. We establish conditions on model Parameters under which equilibrium is or is not efficient. For inefficient equilibria, we quantify the extent of the inefficiency. Moreover, we study the relation between the number of players and the degree of inefficiency. We find that inefficient equilibria become more inefficient the more players there are. Moreover, the parameter region in which an efficient equilibrium is possible shrinks when the number of players increases.

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 $$\delta $$ź, the game ends during any time period $$t

A non-cooperative mechanism for the Shapley value of airport problems

In this paper we address the question of how to allocate the total cost of building and maintaining an airport runway among its users based on a non-cooperative approach. We present a non-cooperative bargaining game with a unique Nash equilibrium outcome whose payoffs are the Shapley value of an airport problem. Furthermore, it is shown that all strategy profiles leading to a subgame perfect equilibrium in these games are also coalition-proof.

Coalitional Bargaining in Networks

We analyze a noncooperative bargaining game with a general coalition structure. In each period an opportunity for a feasible coalition to form arises according to a stochastic process, and a randomly selected agent in the coalition makes a take-it-or-leave-it offer to the other agents in the coalition. We develop a new technique based on convex programming to characterize the unique stationary equilibrium payoff of the game. We apply the framework to various settings including trading networks with middlemen and cooperation networks with overlapping communities. In these applications, feasible coalitions are determined by an underlying network structure. We study the effect of the underlying network on the pattern of trade and show how an agent’s payoff is related to her position in the network.

Procedural fairness and redistributive proportional tax

We study the implications of procedural fairness on the share of income that should be redistributed. We formulate procedural fairness as a particular non-cooperative bargaining game and examine the stationary subgame perfect equilibria of the game. The equilibrium outcome is called tax equilibrium and is shown to be unique. The procedurally fair tax rate is defined as the tax rate that results in the limit of tax equilibria when the probability that negotiations break down converges to zero. The procedurally fair tax rate is shown to be unique. We also provide a characterization of the procedurally fair tax rate that involves the probability mass of below average income citizens and a particular measure of the citizens’ boldness. This characterization is then used to show that in a number of interesting cases, the procedurally fair tax rate equals the probability mass of below average income citizens.

Insurance bargaining under ambiguity

This paper investigates the effects of an increase in ambiguity aversion and an increase in ambiguity in an insurance bargaining game with a risk-and-ambiguity-neutral insurer and a risk-and-ambiguity-averse client. Both a cooperative and a non-cooperative bargaining game are examined. We show that, in both games, full coverage is optimal in the presence of ambiguity, and that the optimal premium is higher in the presence of ambiguity than in the absence of it. Furthermore, the optimal premium will increase with both the degree of ambiguity aversion and an increase in ambiguity.

Reliable resources brokering scheme in wireless grids based on non-cooperative bargaining game

Wireless computational grids are evolving due to rapid growth in wireless devices to provide any time any where computing and communication services. Wireless devices are considered as important resources for job execution in a wireless grid. However, they are unreliable due to unstable wireless connections, frequent mobility, and device resource constraints such as limited processing capacity, limited battery life, low communication bandwidth, etc. Consumers and providers in a wireless grid have potential conflicting interests: consumers prefer reliable resources at minimum cost for job execution whereas providers prefer efficient utilization of resources with a maximum profit. Hence it is necessary to design a resource brokering mechanism that assures job(s) execution and satisfies needs of consumers and providers. This paper proposes a software agent based resource brokering scheme that employs a resource brokering agency consisting of a set of software agents which discover and recommend reliable devices, negotiate resource cost using non-cooperative bargaining game, and schedule jobs. Device reliability is modeled by using parameters like processing rate, memory, bandwidth and battery power. Discount function is employed in bargaining game based on job deadline, previous offers of an opponent, and dynamics in the grid market. Adaptive negotiation process is applied by exercising different discount strategies (aggressive or conservative or linear) based on the negotiation status of a player. The scheme is simulated to evaluate performance parameters like resource utilization rate, expected profit, job completion time and job execution rate. We observed that the proposed scheme performs better than the existing resource brokering scheme.