Noncooperative Bargaining Research Articles

An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value

We experimentally compare two well-known mechanisms inducing the Shapley value as an ex ante equilibrium outcome of a noncooperative bargaining procedure: the demand-based Winter's demand commitment bargaining mechanism and the offer-based Hart and Mas-Colell procedure. Our results suggest that the offer-based Hart and Mas-Colell mechanism better induces players to cooperate and to agree on an efficient outcome, whereas the demand-based Winter mechanism better implements allocations that reflect players' effective power, provided that the grand coalition is formed.

Non-cooperative Bargaining and Collusion Formation Through Communication Networks

Non-cooperative Bargaining and Collusion Formation Through Communication Networks

The effect of choosing a proposer through a bidding procedure in implementing the Shapley value

We experimentally compare simplified versions of two mechanisms that implement the Shapley value as an (ex ante) equilibrium outcome of a noncooperative bargaining procedure: one proposed by Hart and Mas-Colell (1996, H-MC) and the other by Perez-Castrillo and Wettstein (2001, PC-W). While H-MC induces the Shapley value only on average, PC-W does so as a unique equilibrium outcome by introducing an additional bidding stage on top of H-MC. We investigate the effect of this additional bidding stage on the resulting outcomes such as the frequency of grand coalition formation, efficiency, and the distance between the realized allocation and the Shapley value. Our experiment shows that H-MC not only results in significantly greater efficiency than PC-W, but also that the average allocation is closer to the Shapley value for those groups that formed the grand coalition. This difference is because those proposers who won the bidding stage in PC-W tend to offer an allocation that favors themselves more often, when compared to allocations proposed by randomly selected proposers in H-MC, and such offers are more likely to be rejected.

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.

Non-Cooperative Bargaining with Unsophisticated Agents

A traditional non-cooperative bargaining situation involves two or more forward-looking players making offers and counteroffers alternately until an agreement is reached, with a penalty according to the time taken by players in the decision-making process. We introduce a game that aids myopic players to reach the equilibrium as if they were forward-looking agents. The key elements of the game are that players are penalized both for their deviation from the previous best-reply strategy and their time taken for the decision-making at each step of the game. It is shown that our game has an equilibrium not only for the traditional processes and utilities used in traditional non-cooperative bargaining literature, but for an expanded and very comprehensive set of stochastic processes (such as Markov processes) and utility functions. Our work not only complements traditional non-cooperative bargaining literature for myopic agents, but also enlarges the class of processes and functions where Rubinstein’s non-cooperative bargaining solutions might be defined and applied.

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.

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.

Bargaining between Agents with Differing Degrees of Risk Aversion

I show that in noncooperative bargaining between two players with risk aversion, the more risk averse player always obtains a larger equilibrium payoff, after controlling for the other sources of advantage in bargaining e.g. patience and order of bargaining. I contrast my result with that of Roth (1985) that a risk averse player is disadvantaged when facing a risk-neutral opponent. A recent result from Rausser and Simon (2016) disputing the adverse connection between Nash bargaining solution and risk aversion is also related with my subgame perfect equilibrium case.

Quality risk in logistics outsourcing: A fourth party logistics perspective

We investigate an outsourcing logistics risk management problem under a principal-agency framework. A fourth-party logistics firm (4PL) deputes a third-party logistics firm (3PL) to complete the tasks received from clients. The 4PL cannot observe the effort/investment level of the 3PL on the delivery quality but only on the ex post delivery quality. Thus, a contract based on delivery quality is proposed to stimulate the 3PL to exert optimal effort/investment for the outsourced task. First, we derive the optimal contract contents both in symmetric and asymmetric information settings and show that in the asymmetric information setting, although a menu of contracts can induce the 3PL to tell the truth, asymmetric efficiency information can lead to a drop in delivery quality as well as in system-wide welfare. Then, to deal with this issue in the asymmetric information setting, we introduce two contracts: noncooperative bargaining and cooperative bargaining contracts. We find that the cooperative bargaining contract can ensure the 3PL exerts the maximum effort/investment level and achieves high-quality delivery and system-wide welfare. Finally, we extend our study to a case with discrete efficiency distribution and analyze various types of contracts as well as their implications.

UNIVERSALISM AND THE VALUE OF POLITICAL POWER

AbstractAlthough legislatures typically use majority rule to allocate a budget in distributive legislation, unanimous consent over the broad allocation of benefits is pervasive. I develop a game‐theoretic model where members strategically interact in a universal coalition to determine allocations, with noncooperative bargaining as a threat point for the breakdown of cooperation. To quantify the effects of political power on the agreed‐upon allocation, I structurally estimate the model using the “Bridge Bill Capital Budget” in 1992. I find that 16.73% of the budget would be allocated differently if allocations were determined only based on actual needs.

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.

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.

Policy Preferences in Coalition Formation and the Stability of Minority and Surplus Governments

In parliamentary democracies, political parties bargain over cabinet portfolios when forming coalition governments. While most of the theoretical literature predicts that only minimal winning coalitions form in equilibrium, the empirical evidence shows that minority and surplus coalitions are about as frequent. In this article, I bridge the gap between the theoretical predictions and the empirical evidence by developing a noncooperative bargaining model in which parties are both office seeking and policy pursuing. Parties bargain over cabinet portfolios, which in turn determines the government policy. Parties are farsighted, and when they coalesce with other parties, they take into account not only the expected cabinet portfolio allocation but also how this allocation would affect the government coalition policy. The model predicts in equilibrium the formation of minimal winning as well as minority and surplus coalitions as a function of a party’s size, ideal policies, and relative preference for policy versus office.

Efficient non-cooperative bargaining despite keeping strategic information private

The preferred method for negotiating joint value-added activities, such as e.g. licensing, co-venturing or supply chain expansion, is cooperative bargaining, where agents act rationally and have perfect information, i.e., information sharing occurs. In such settings, however, stronger partner often insist on keeping their valuable information private and thus cooperative bargaining cannot occur due to the lack of information sharing. Though, non-cooperative bargaining is usually assumed to be inefficient. Based on a game-theoretic real options model, we develop a contractual solution that allows the proposer to keep its valuable information private while at the same time motivates the other partner to act in a timely and efficient manner, that is, to be Pareto-efficient.

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.

British tax credit simplification, the intra-household distribution of income and family consumption

The UK Government enacted simplification of its tax credit system in 2003. An interesting consequence of the reform is that tax credit payments were split between partners in couples, causing a rare wallet to purse transfer. This paper presents evidence on family spending from the reform, using quasi-likelihood techniques, for a sample of low income couples with children. A key result is the absence of reform effects at the level of eleven broad spending categories. However, this masks important within category changes. For specific expenditure items, significant increases are observed amongst household public goods that have an important child development aspect; whilst spending decreases are observed amongst household public goods that disproportionately benefit parents. Results are contrasted to earlier findings from 1970s child benefit reforms. The effects are consistent with a non-cooperative bargaining framework, in which partners differ in their relative preference for different household public goods.

Developing a stochastic conflict resolution model for urban runoff quality management: Application of info-gap and bargaining theories

Summary In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.

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