Bargaining Model Research Articles

Information problems and Russia's invasion of Ukraine

This paper explores the role of asymmetric information as a cause of Russia's 2022 invasion of Ukraine. In the classic bargaining model of war, negotiations break down when one side privately believes that it is sufficiently more likely perform better in battle than the other side expects. There is strong evidence that this mechanism was at play on the eve of the invasion. Chronic problems with Russian civil–military institutions created both an army unprepared for the conflict and a lack of awareness of this within the Kremlin. In contrast, Ukraine had reports of these problems and also had private information regarding its own resolve. Consequently, the Kremlin's demands on the eve of the conflict exceeded what Ukraine was willing to concede. Russia invaded as a result.

Who benefits? Experimental evidence on Saudi women’s take-up of unemployment assistance

Does a woman’s take-up of government benefits vary with her perception of how they will be shared within the household? Using randomized assignment to alternative information treatments, we examine this question in the context of Saudi women’s willingness to apply for unemployment assistance (Hafiz). We compare the take-up among women who receive no program information to three groups: those who receive information on program eligibility conditions (Eligibility group) and those who receive additional information that their registration status is broadly confidential (Privacy group) or that they fully control registering and accessing benefits (Agency group). Three months later, the treatments, on average, doubled Hafiz applications, with the treatment impacts largest for the Agency group. Women from poorer households and married women are most responsive to the Agency and Privacy interventions respectively. These findings are consistent with collective household bargaining models where family members’ spending preferences differ; we predict larger treatment impacts when there is more competition for resources.

The influence of gender specific decisions on household technology choice within the farming households in central Uganda

How households make decisions, who influences decision making and how members bargain over resources and opportunities greatly affects the livelihood and wellbeing of members within a given household. This study sought to understand gender specific decisions and their influence on household technology choice, packaging and adoption of agricultural technologies. Growing Bananas with Trees and Livestock (GBTL) technology system was implemented by National Agricultural Research Organisation and Bioversity International in three districts of Central Uganda: Kiboga, Nakaseke and Ssembabule. Using Principal Component Analysis (PCA) and Cluster Analysis (CA), typologies were created in which two distinct clusters of farming households were revealed. Using a bargaining model of technology adoption, three types of households were identified; male and female only, female only and male only headed households. For technology uptake, either a single component, two components or all components of a technology was adopted. Results indicated that Household size, age, land owned, labour and gender composition of the household positively influenced the adoption of the technology. Farm households were able to take up and adopt components of the technology that were equivalent to the available household resources. Technology choice and adoption was influenced by available land, labor and household objectives (food, income and nutrition security). Households' ability to avert the loss of production and/or assets was very varied and depended on household size. For non-business home expenses, decisions followed a gendered perspective where households with both male and female, had more participants involved in household decision making, households make decision jointly when it comes to purchases and sales. Banana plantations establishment and management was for the spouse. Livestock production was initiated and managed by the household heads. Individual decisions were influenced by age of the household head, livestock owner. Joint household’s decision making was significant on purchases, sales of inputs and outputs, land ownership, and were influenced by household size and farm size. This study brings out important policy implications that in order to ensure widespread adoption of improved technologies, there should be equitable access to complementary inputs, especially land and labour for females. And technology packaging should take into consideration the gender specific decisions for sustainable agricultural development. Key words: Decision making, Technology choice, adoption, Coffee banana farming system, Gender

Atomic Signaling: Exploring Likelihood of Success and Military Necessity through the Bargaining Model of War

Did the decision to drop the atomic bomb on Hiroshima and Nagasaki during World War II meet the military necessity and likelihood of success criteria of the Just War Theory? Many scholars and ethicists have argued that they did not. We examine the decision through the rationalist models of war preferred by international relations theorists. We introduce a simple version of the bargaining model of war and tease out its essential differences with the models of war (and, therefore, military necessity) used by most Just War Theorists. Then, we reconstruct the decision to drop the bomb on Japan, focusing especially on information states, preference sets, and operational realities, to show that, if the dropping of the atomic bomb on Hiroshima and Nagasaki does not meet military necessity and likelihood of success criteria, no other kind of military activity can.

Distributed optimization of station-network collaborative operation and alliance benefit allocation for integrated energy system

With the increasingly urgent need to build a clean and efficient energy system, the interaction between energy station and networks is closer and the coupling relationship becomes more complex. To break energy barriers in independent solution of energy subsystems and solve the problem of privacy disclosure caused by centralized solution of integrated energy system, a distributed optimization of station-network collaborative operation and alliance benefit allocation for integrated energy system is provided. Firstly, a Nash bargaining model of multi-stakeholder cooperation is constructed based on cooperative game theory; Secondly, the nonconvex and nonlinear Nash bargaining model is equivalent converted into alliance economic optimization subproblem and energy transaction dynamic pricing subproblem for the convenience of solution; Thirdly, a distributed optimization architecture for subproblems is constructed based on alternating direction method of multipliers with an adaptive dynamic penalty factor updating strategy. Finally, the effectiveness of the proposed method is verified by a numerical example and the simulation results show that privacy information and independence in decision-making of each stakeholder are protected. The convergence speed and local refine search ability are improved by the adaptive dynamic penalty factor updating strategy. What’s more, more benefits are obtained than independent optimization, and higher satisfaction and richer information based on dynamic pricing are got than the widely used Shapley value, which is practical significance to improve the enthusiasm of all stakeholders to participate in energy trading and promote energy transformation.

Uncertainty in crisis bargaining with multiple policy options

AbstractFormal models commonly characterize interstate bargaining as dichotomous, ending in either war or peace. But there are many forms of coercion—including supporting rebel groups, sanctions, and cyberattacks. How does the availability of intermediate policy options affect the incidence of war and peace? We present an analysis of crisis bargaining models with intermediate policy options that challenges conventional results about the relationship between private information and negotiation outcomes. In our “flexible‐response” modeling framework, unlike in traditional crisis bargaining models, we find that greater private war payoffs may be associated with a lower probability of war or worse settlement values. When intermediate options are available, the relationship between the private efficacy of war and the private efficacy of these other options largely determines equilibrium outcomes. By utilizing the tools of mechanism design, we derive game‐form–free results on how private information shapes international conflict, regardless of the precise negotiating protocol.

Maternal relative income, bargaining power, and children's education expenditure

This study presents a household bargaining model to theoretically examine the logical mechanisms by which maternal relative income influences children's education expenditure. The theoretical findings demonstrate that an increase in maternal relative income can enhance children's investment in education through both the income effect and bargaining effect. To validate the theoretical model, empirical tests are conducted using panel data from the China Family Panel Studies (CFPS) covering the period from 2010 to 2018. The findings demonstrate a significant and robust positive influence of maternal relative income on children's education expenditure, even after conducting rigorous robustness tests and addressing potential endogeneity issues. Heterogeneity analysis reveals that the increase in maternal relative income particularly benefits boys, younger children, and those with fewer siblings. Moreover, households residing in northern China and high-income households observe a more substantial rise in their children's education expenditure as a result of an increase in maternal relative income. Mechanism tests indicate that the impact of maternal relative income on children's education expenditure primarily stems from both the income effect and bargaining effect.

Reference points in sequential bargaining: theory and experiment

AbstractWe introduce loss aversion in an infinite‐horizon, alternating‐offers model. When outside options serve as reference points, the equilibrium of our model follows that of the standard Rubinstein bargaining model (i.e., outside options do not affect the equilibrium unless they are binding). However, when reference points are given by the resources that players contribute to the pie, the bargaining outcome changes such that a player's share increases in her contribution. We test our model's predictions in the laboratory. As predicted, only binding outside options affect the division of the pie. Data also show that contributions matter for bargaining outcomes when they are activated as reference points, but not quite as predicted by our theory. Proposers gain a higher share of the pie only when they have contributed a higher share than the opponent has.

Research on Energy Management Strategy for Extended‐Range Electric Vehicle Based on Bargaining Game

To improve the fuel economy and battery life of extended‐range electric vehicles (EREVs), an energy management strategy (EMS) based on the bargaining game (BG) is proposed. This strategy optimizes the overall economy by optimizing power allocation. First, a bargaining model for EREVs is developed. The model considers the auxiliary power unit (APU) and the battery as two parties of the game. The power allocation between the APU and the battery optimizes both the fuel consumption and the battery life. And it also improves the overall benefit of the vehicle. Second, the effect of the discount factor on the control results is analyzed to obtain the best optimization results. Finally, compared to the thermostat strategy and the dynamic programming‐based strategy, the proposed BG‐based strategy reduces fuel consumption by 27.6% and 1.4% under the World Light Vehicle Test Procedure and reduces the effective ampere‐hour fluxes by 62.7% and 14.6%. Under the China Light‐duty Vehicle Test Cycle, it reduces fuel consumption by 32.5% and 0.5% and reduces the effective ampere‐hour fluxes by 56.8% and 27.5%. The simulation results manifest the excellent performance of the proposed BG‐based EMS.

Social partnership, company-level collective bargaining and union revitalization in Ireland

This article explores recent trade union efforts in Ireland to re-engage activists and members and promote revitalization following the termination of a 22-year period of tripartite social partnership. It analyses four case studies of major unions’ strategies to involve activists and members in a workplace-anchored model of firm-level collective bargaining. The findings indicate that decentralized bargaining has become the preferred model of pay determination for Irish unions, and they express little interest in returning to national-level centralized bargaining. Union leaders are enthusiastic about company-level bargaining primarily for three reasons. First, it revitalizes unions by sustaining and expanding union membership at the workplace. Second, it supports local bargaining arrangements that produce tangible benefits for workers, showcasing the effectiveness of unions in advocating for their members. Third, workplace arrangements enhance union influence over management decision-making, both directly through firm-level collective bargaining and indirectly by fostering incentives for continuous dialogue and information exchange.

Do prosecutors induce the innocent to plead guilty?

AbstractThe implications of a strategic model of plea bargaining are threefold. First, plea bargaining unequivocally increases wrongful convictions. Next, partial bans on plea bargaining reduce the frequency of wrongful convictions, and the reduction rises with the strength of the ban. Lastly, police share an important role in minimizing wrongful convictions.

Efficient virtual power plant management strategy and Leontief-game pricing mechanism towards real-time economic dispatch support: A case study of large-scale 5G base stations

Amidst high penetration of renewable energy, virtual power plant (VPP) technology emerges as a viable solution to bolster power system controllability. This paper integrates a novel flexible load, 5G base stations (gNBs) with their backup energy storage systems (BESSs), into a VPP for power system real-time economic dispatch (RTED). Leveraging BESSs dispatchable capacity, the VPP offers power support and gains economic incentives, where the dispatchable capacity is estimated based on distribution network reliability and gNB availability requirements. Then, an efficient and refined VPP management strategy is proposed, where numerous gNBs are aggregated into limited number of virtual generators (VGs). The VPP dispatchable capacity can be efficiently and accurately evaluated via VGs states. Each VG is assigned a control cost function, enabling optimal control decisions resembling power system RTED, to minimize overall VPP control costs. Finally, a power support and incentive determination mechanism is presented based on the Leontief union bargaining model, ensuring reciprocal transactions between VPP and power system. To solve the Leontief model and address information privacy issues between the two parties, a distributed iterative algorithm is developed. Simulations based on actual data and IEEE 118-bus system illustrate that the proposed approach can smoothen intra-day load profiles, achieving mutual economic benefits for the power system and VPP without compromising the security of 5G network operations.

China's National Reserve Forest Project contribution to carbon neutrality and path to profitability

The National Reserve Forest Project (NRFP) is a forestry project launched by China in 2013 to ensure the safety of timber supply and create a carbon sink, which can contribute to China's future carbon neutrality goals. To evaluate the carbon neutral contribution and carbon sink benefits of the NRFP, it is necessary to estimate the carbon sink amount, carbon sink cost, and carbon sink price. A combined method, modified Hartman model, and Rubinstein-Stahl bargaining model were used to estimate and analyze the carbon sink amount, carbon sink cost, and carbon sink price of NRFPs from several typical NRFP zones to the nationwide level. Results show that: (1) if the yearly construction area of the NRFP keeps stable at 10.2 × 105 ha in the future, the carbon sink of NRFP will account for about 17.32%, 28.35%, and 80.00% of total carbon emissions in 2060 under low-, middle-, and high-policy scenarios, respectively, representing an increase compared to the current level of approximately 16%; (2) the weighted average carbon sink cost of NRFP is estimated to be 95.16 CNY/t CO2 e (lower than the average carbon sink cost of 150 CNY/t CO2 e), and several measures such as applying Public-private partnership investment (PPP), increasing project operation duration, and choosing construction areas with low farmland benefit can help further reduce carbon sink cost of NRRP; (3) the reasonable carbon sink price should fall between the carbon sink cost and marginal carbon emission reduction cost of enterprises, and increasing the carbon sink price has a positive impact on NRFP construction. NRFPs suffer economic losses in the present carbon trade market, but they will gradually become profitable with the rising carbon sink price in the future. Therefore, it is imperative to maintain or gradually expand the construction area, provide more financial support, and improve the carbon trading market of NRFPs.

A Comment on: “Walras–Bowley Lecture: Market Power and Wage Inequality” by Shubhdeep Deb, Jan Eeckhout, Aseem Patel, and Lawrence Warren

A burgeoning literature in labor economics is focused on modeling employer labor market power, generally finding nontrivial estimates of monopsony power. A smaller literature also simultaneously incorporates product market power. Deb, Eeckhout, Patel, and Warren (2024) is an example of applying an oligopoly‐oligopsony model to the U.S. labor market, arguing for important effects on wage levels and inequality from rising market power. I support combining IO and labor as a fruitful way of studying wages and business dynamism, but argue for looking more broadly at (i) differential degrees of employer power in labor and product markets; (ii) investigating the dynamic sources of markups (e.g., through innovation), and (iii) considering wage bargaining models, not just wage posting models, which have some starkly different implications for wage setting.

The role of the judge in the European plea bargaining procedures: Three models compared

This article examines the role of the judge in ‘prosecutor-centred’, ‘law-centred’ and ‘judge-centred’ models of plea bargaining in the European context. A comprehensive study regarding the judicial role in plea bargaining is necessary, since the principle of double control has frequently been neglected in negotiated case dispositions, and in the literature it has often been suggested that more robust judicial control of plea bargaining should be in place. Instead of a pan-European overview, our article focuses on the different models of plea bargaining, particularly in the example of the Swiss abbreviated proceedings, the German confession bargaining and the English sentence discount. In order to put the judge's role into context, the article first introduces the contours of each model before analysing the role of the judge in these proceedings. In conclusion, the article compares the models discussed, which would provide a baseline for assessing the judicial role in plea bargaining.

Water Resources Allocation in a Transboundary River Based on a Rubinstein Bargaining Model

Water Resources Allocation in a Transboundary River Based on a Rubinstein Bargaining Model

Green Investment Decisions and Coordination in a Green Agri-Product Supply Chain considering Risk Aversion and Bargaining Power under Different Channel Power Structures

With eco-friendly green agriculture becoming the development trend of modern agriculture, how to make green investments and how to coordinate the supply chain become the key issues of agricultural green development. Using game theory and optimization theory, this paper studies the green investment decision in a two-echelon agricultural supply chain composed of a risk-averse farmer and a risk-neutral retailer under different power structures including three kinds of decentralized decision making and three kinds of cooperative decision making and conducts the supply chain coordination based on generalized Nash bargaining model. The results show that under decentralized decision making, Nash vertical, farmer-led, and retailer-led maximizes green investment level, the expected utility of farmer and retailer, respectively. In addition, the cooperative decision increases the marginal revenue, sales price, and the expected utility of the retailer and decreases the expectations of farmers. Except for retailer-led cooperative decisions, all cooperative decisions have increased the level of green investment and wholesale prices; among the six decision models, the green investment level is negatively correlated with risk aversion, while it is positively correlated with the cost-sharing contract. The optimal cost-sharing ratio is positively correlated with risk aversion and bargaining power. The cost-sharing contracts are invalid when farmers have full bargaining power. Numerical analysis shows that a cost-sharing contract with equal bargaining power can achieve perfect coordination in the supply chain.

'Til Dowry Do Us Part: Bargaining and Violence in Indian Families

Abstract We develop a non-cooperative bargaining model with incomplete information linking dowry payments, domestic violence, resource allocation between a husband and a wife, and separation. Our model generates several predictions, which we test empirically using amendments to the Indian anti-dowry law as a natural experiment. We document a decline in women's bargaining power and separations, and a surge in domestic violence following the amendments. These unintended effects are attenuated when social stigma against separation is low and, in some circumstances, when gains from marriage are high. Whenever possible, parents increase investment in their daughters' human capital to compensate for lower dowries.

Pure strategy Nash equilibria for bargaining models of collective choice

This paper considers pure strategy Nash equilibria of non-cooperative legislative bargaining models. In contrast to existing legislative bargaining models, we derive legislators behavior from stochastic utility maximization. This approach allows us to prove the existence of a stationary Pure Local and Global Nash Equilibrium under rather general settings. The mathematical proof is based on a fixed point argument, which can also be used as a numerical method to determine an equilibrium. We characterize the equilibrium outcome as a lottery of legislators’ proposals and prove a Mean Voter Theorem, i.e., proposals result dimension-by-dimension as a weighted mean of legislators’ ideal points and are Pareto-optimal. Based on a simple example, we illustrate different logic of our model compared to mixed strategy equilibrium of the legislative bargaining model suggested by Banks and Duggan (Am Polit Sci Rev 94(1):73–88. https://doi.org/10.2307/2586381, 2000).

Ultimatum bargaining with envy under incomplete information

We propose an ultimatum bargaining model in which the parties experience an envy-based externality that is private information. Our results indicate that there is a threshold for the proposer’s envy which determines whether there will be either a perfectly equitable, certain agreement or an uncertain, inequitable agreement, and that this threshold rises as the distribution of the responder’s envy level improves in a first-order stochastic-dominance sense. In addition, conditionally on the scenario ruling out a perfectly equitable agreement, we show that the proposer’s envy level plays a dual role: (i) it increases the probability of a negotiation breakdown, and (ii) it constitutes a source of bargaining power. Numerical simulations also allow us to explore some properties of the role played by the responder’s envy and by changes in the envy distributions of the two players. Overall, our theoretical results are consistent with the main evidence from ultimatum experiments conducted in behavioral and neuroscience settings. In addition, we provide testable implications of our model for future experiments.