Sequential-move Game Research Articles

Strategic coopetition among transportation service providers considering supply–demand congestion effects and asymmetric bargaining power

The phenomenon of transportation service providers (TSPs) engaging in both competition and cooperation, commonly referred to as coopetition, has become increasingly prevalent in the transportation market. This is driven by the rapid advancements in information technology and sharing economy. In practice, competitive TSPs can engage in a resource exchange scheme to share their resources to improve their service quality. However, such a resource exchange scheme may not be sustained since the service prices and profits will be further changed due to the competition in the end market. This study proposes a two-stage sequential-move game to characterize the coopetition problem between TSPs, wherein the first-stage resource exchange problem is modeled with a Nash bargaining game, and the second-stage pricing problem is modeled with a non-cooperative Nash game. Different from prior studies, our model incorporates the supply–demand congestion effects and the asymmetric bargaining power of TSPs. The subsequent impacts on social welfare, TSPs, and end users are investigated. Analytical results show that only when the unit price of the exchanged resources decreases in the exchanged resource quantity will the resource-exchange scheme succeed. Furthermore, we find that TSPs prefer to leave some “buffer zone” in between to avoid fierce competition with price wars.

Strategic investment in charging infrastructure: Sharing costs or taking over?

The substantial upfront investment required for the installation of charging infrastructure deters many potential charging station adopters, such as shopping mall operators and real estate owners, from independently undertaking the deployment. Some government agencies (Govs) offer subsidies as a means of encouraging the extensive implementation of charging infrastructure. Nonetheless, this approach is not viable in the long term owing to the constrained public budget. An improper subsidy scheme may induce adopters to become overly reliant on Govs support. To tackle this issue, some local Govs have initiated cost-sharing schemes with adopters who are willing to install chargers. In a typical cost-sharing scheme, the Gov initially assigns the cost-sharing rate to adopters. Subsequently, the adopters determine the quantity they are willing to install through cost-sharing. Despite the potential benefits of the scheme, there are still some challenges: (i) The public budget is limited, (ii) The charging infrastructure penetration goal is uncertain, (iii) Adopters are heterogeneous and their decisions are interdependent, and (iv) Adopters possess dissimilar beliefs regarding the policy of the Gov. These factors could potentially prompt certain adopters, who possess the financial capability to cover the installation expenses, to employ deceptive tactics aimed at persuading the government to assume the entire cost. In consideration of the aforementioned challenges, we propose a sequential-move game model to assess the strategic interactions between the Gov and charging station adopters. We demonstrate that there exists a many-to-one mapping between the optimal cost-sharing rates and the optimal number of installed chargers. Then, we derive the conditions when the Gov withdraws from the market and when it intervenes to share costs with adopters. The results suggest that a reduction in the level of competition intensity leads to an increased probability of adopters engaging in the cost-sharing scheme. This is in contrast to scenarios where policy uncertainty increases or where the correlative effects arise among all adopters’ strategies.

Electricity grids and geopolitics: A game-theoretic analysis of the synchronization of the Baltic States’ electricity networks with Continental Europe

Can supply of electricity be used as an energy weapon? This question rises in importance as more countries trade electricity across borders to smooth out grid stability issues and improve cost-efficient dispatching across large geographic areas. In the context of the Baltics’ disentanglement from the BRELL (Belarus, Russia, Estonia, Latvia, and Lithuania) electricity grid and synchronization with Europe, we develop a game-theoretic model and examine the strategies of the involved parties in light of the potential for electricity trade to be used as a geopolitical weapon. We conceptualize the process of the synchronization project as a sequential-move game between three actors (Russia, the Baltic states, and the EU-U.S.). Our findings suggest that, in large part due to reputational concerns, Russia is unlikely to cooperate in the synchronization process. Instead, our model predicts that Russia will not wait for the Baltic states to complete their synchronization with the European grid before disconnecting them from the BRELL system. Direct Russian cyberattacks against Baltic grids are not implemented and the Baltics do not have to make concessions, provided that Western allies signal a strong likelihood of deterrent retaliation. We offer policy recommendations for Europe, Russia and the Baltic states.

Advance selling strategy of fresh products under two contracts

PurposeThis paper analyzes the advance selling and pricing strategies of fresh products supply chain where the e-retailer provides wholesale contract or agency contract to the fresh products supplier.Design/methodology/approachThis paper constructed a two-period sequential-move game of fresh products supply chain members.FindingsThis analysis showed that the supply chain members had different preferences for contracts under different market conditions. The advance selling of fresh products was not a decision of the seller, but also required the support of other supply chain members. And the advance selling strategy was not always beneficial to all supply chain parties. Under the two contracts, there were market conditions in which the profits of supply chain members were Pareto-improved through the implementation of advance selling.Research limitations/implicationsThe model presented in this study focuses solely on the context of monopoly, overlooking the competition from alternative suppliers or retailers. Consequently, exploring the competitive landscape within the fresh products supply chain, particularly in relation to pre-sale pricing, emerges as a crucial avenue for further investigation. By employing empirical research methods, valuable insights are gleaned, thereby significantly augmenting the existing body of relevant theories.Practical implicationsThe decision to pre-sell fresh products should be based on market conditions. Supply chain members can control production costs and fresh products circulation losses to maximize profits.Originality/valueFrom the perspective of game theory, this study analyzed the optimal advance selling and pricing strategies of fresh products supply chain members under two kinds of contracts. These results can provide practical implications for fresh products suppliers and e-retailers.

Mechanism Design with Sequential-Move Games: Revelation Principle

Mechanism Design with Sequential-Move Games: Revelation Principle

Strategic collaboration between land owners and charging station operators: Lease or outsource?

Many regions of the world aim to phase out conventional private gasoline cars within ten years, requiring imminent expansion of the electric vehicle (EV) charging infrastructure. However, because of high installation and maintenance costs, many landowners (LOs), such as shopping malls and commercial building owners, hesitate to install and operate large-scale EV charging facilities of their own volition. In light of this reason, government-led investment is widely provided in many cities, in which local governments provide subsidies to or directly invest in the installation of EV charging facilities. However, this mode cannot be sustained in the long run. As the charging infrastructure market grows, many charging station operators (CSOs), who specialize in EV charging facility installation and operation, have emerged in recent years. These CSOs rent parking spaces from LOs to operate their charging business, which can potentially benefit LOs by attracting more EV drivers to patronize LOs. This parking-charging integration scheme (P&C scheme) builds a symbiotic relationship between LOs and CSOs. However, such schemes may have negative impacts on LOs. Allocating parking spaces to CSOs will increase the time general consumers without charging needs spend searching for parking, which will reduce the number of general consumers. If the newly attracted EV drivers only charge but do not consume in the LO, the LO might not be better off by participating in this scheme. To analyze the economic viability of the P&C scheme and the resulting impact on consumers, we develop a sequential-move game model, taking into account the responses of general consumers and EV drivers. We analytically prove the existence and uniqueness of the market equilibrium and derive the feasibility conditions for this scheme. Interestingly, we find that when the proportion of charging drivers who choose to patronize the LO is high, the LO is willing to reward the CSO for operating the charging service. A realistic P&C example is also presented to demonstrate our analytical insights.

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

Competitive CSR in a strategic managerial delegation game with a multiproduct corporation

We study the firm’s strategic choice of corporate social responsibility (CSR) in a managerial delegation framework where a multiproduct corporation competes against a single plant firm. We examine simultaneous-move versus sequential-move in output choices when CSR’s strategic level is simultaneously chosen in the first stage. We show that both firms adopt (asymmetric) CSR in a simultaneous-move game, whereas only the follower firm adopts CSR (but not the leader firm) in sequential-move games. In an endogenous timing game in output choices, we also show that a simultaneous-move is an equilibrium when the products are substitutes or weak complements, while a single plant firm’s leadership is otherwise wherein the multiproduct corporation might choose negative CSR. Our findings can explain the observed phenomenon of different industries in which firms’ CSR activities are more or less (even non-CSR or negative CSR), commonly widespread in the real world. It also partially helps us understand CSR’s strategic motives and its policy relations with the firm’s profits.

Sourcing under competition: The implications of supplier capital constraint and supply chain co-opetition

This paper investigates a manufacturer’s strategic sourcing and supplier financing strategies under downstream horizontal competition and co-opetition. When the manufacturer and the rival engage in a simultaneous-move game, we show that the manufacturer should always exclusively source from and offer finance to a cost-advantageous supplier if the latter is severely capital-constrained. If the supplier is moderately capital-constrained, however, the manufacturer’s preferred sourcing strategy depends on the type of the backup supplier, which leads to a horizontal competition or co-opetition structure. We also examine the robustness of the results by studying the sequential-move game.

A Note on Stackelberg Mixed Triopoly Games with State-Owned, Labor-Managed and Capitalist Firms

This paper investigates three sequential-move games with a capitalist firm, a labor-managed firm and a state-owned firm. The first game is as follows. In stage one, the capitalist firm chooses its output level. In stage two, the other firms choose their output levels simultaneously and independently. In stage three, the market opens and each firm sells its entire output. The structures of the second and third games are nearly identical and differ only in order in which the firms choose output levels in the first two stages. The paper discusses the equilibrium outcomes of the three sequential-move games.

An endogenous-timing conflict game

Abstract We present an endogenous-timing conflict game of incomplete information under strategic complementarity. The model predicts multiple equilibria, in which the outcome follows either a simultaneous move game (Baliga and Sjostrom, 2004) or a sequential game, which improves social welfare. We study the three families of games in the laboratory using gender-balanced sessions. Our results suggest that: (i) social welfare is higher in the endogenous-timing and sequential games compared to the simultaneous game; (ii) men and women make similar decisions in the simultaneous and sequential-move games; and (iii) in the endogenous-timing game women are less willing to commit to the risky action.

Functional magnetic resonance imaging multivoxel pattern analysis reveals neuronal substrates for collaboration and competition with myopic and predictive strategic reasoning.

Competition and collaboration are strategies that can be used to optimize the outcomes of social interactions. Research into the neuronal substrates underlying these aspects of social behavior has been limited due to the difficulty in distinguishing complex activation via univariate analysis. Therefore, we employed multivoxel pattern analysis of functional magnetic resonance imaging to reveal the neuronal activations underlying competitive and collaborative processes when the collaborator/opponent used myopic/predictive reasoning. Twenty‐four healthy subjects participated in 2 × 2 matrix‐based sequential‐move games. Searchlight‐based multivoxel patterns were used as input for a support vector machine using nested cross‐validation to distinguish game conditions, and identified voxels were validated via the regression of the behavioral data with bootstrapping. The left anterior insula (accuracy = 78.5%) was associated with competition, and middle frontal gyrus (75.1%) was associated with predictive reasoning. The inferior/superior parietal lobules (84.8%) and middle frontal gyrus (84.7%) were associated with competition, particularly in trials with a predictive opponent. The visual/motor areas were related to response time as a proxy for visual attention and task difficulty. Our results suggest that multivoxel patterns better represent the neuronal substrates underlying the social cognition of collaboration and competition intermixed with myopic and predictive reasoning than do univariate features.

An Endogenous-Timing Conflict Game

We present an endogenous-timing conflict game of incomplete information under strategic complementarity. The model predicts multiple equilibria, in which the outcome follows either a simultaneous move game (Baliga and Sjostrom, 2004) or a sequential game, which improves social welfare. We study the three families of games in the laboratory using gender-balanced sessions. Our results suggest that: (i) social welfare is higher in the endogenous-timing and sequential games compared to the simultaneous game; (ii) men and women make similar decisions in the simultaneous and sequential-move games; and (iii) in the endogenous-timing game women are less willing to commit to the risky action.

Empirical Evidence on Repeated Sequential Games

Sequentiality of moves in an infinitely repeated prisoner’s dilemma does not change the conditions under which mutual cooperation can be supported in equilibrium as compared to simultaneous decision-making. The nature of the interaction is different, however, given that the second mover in a sequential-move game does not face strategic uncertainty in the stage game. We study in an experiment whether sequentiality has an effect on cooperation rates. We find that with intermediate incentives to cooperate, sequentiality increases cooperation rates by around 40 percentage points after learning, whereas with very low or high incentives to cooperate, cooperation rates are respectively very low or high in both settings.

The value of leading customers in a crowdfunding-based marketing pattern.

Crowdfunding is gradually becoming a modern marketing pattern. By noting that the success of crowdfunding depends on network externalities, our research aims to utilize these network externalities to provide an applicable referral mechanism in a crowdfunding-based marketing pattern. In the context of network externalities, measuring the value of leading customers is chosen as the key to coping with the research problem, as the leading customers are considered to be critical in forming a referral network. Accordingly, two sequential-move game models (i.e., the basic model and the extended model) were established to measure the value of leading customers, and a matrix transformation process was adopted to solve the model by transforming a complicated multisequence game into a simple simultaneous-move game. Based on the defined value of leading customers, a network-based referral mechanism was proposed that explores exactly how many awards should be allocated along the customer sequence to encourage the leading customers to provide a successful recommendation, and this demonstrates two general rules of awarding the referrals in our model setting. Moreover, the proposed solution approach helps to deepen the understanding of the effect of the leading position, which is meaningful for designing a greater number of referral approaches.

Strategic Emission Fees: Using Green Technology to Deter Entry

We consider a sequential-move game in which a polluting monopolist chooses whether to acquire a green technology, and a potential entrant responds deciding whether to join the market and, upon entry, whether to invest in clean technology. Our paper compares two models: one in which environmental regulation is strategically set before firms’ decisions; and another where regulation is selected after firms’ entry and investment decisions. We show that a proactive regulation that strategically anticipates firms’ behavior can implement different market structures. In particular, policy makers can choose emission fees to induce competition and/or investment in clean technology, giving rise to market structures that maximize social welfare.

Strategic spending in federal governments: theory and evidence from the US

ABSTRACTPast research on the allocation of federal resources to localities has failed to account for the interaction between federal and state governments. Here a sequential-move game of such interaction is developed, where state governments behave like political surrogates for the federal government when they are politically aligned, while they engage in political competition when not. The model predicts that aligned states increase the funding of aligned localities, while the federal government increases the funding of aligned localities only within nonaligned states. Using data from the Census of Governments 1982–2002 and a difference-in-difference strategy reveals that such predictions are upheld by the data. My findings find a limit to the benefits of decentralization. Although the standard view is that it removes political power from the center, I find that decentralization could concentrate such power more at local level, which may give the President political advantages within unaligned states through aligned localities.

Leadership in Tax Competition with Fiscal Equalization Transfers

Abstract We propose a timing game of asymmetric tax competition with fiscal equalization scheme. The study finds that governments tend to play a sequential-move game as the scale of equalization transfer increases, which explains the emergence of tax leaders in tax competition. The presence of a tax leader is likely to exacerbate capital misallocation among countries, suggesting that equalization transfers aimed at narrowing the interregional fiscal gap might cause an inefficient capital allocation.

A model of terrorism and counterterrorism with location choices

We study a model of terrorism and counterterrorism with three geographic target locations, in which the last location is chosen by the terrorists and is unknown to the defender. We find the choice of location and defender’s allocation of defensive resources to depend on whether the first two locations are attacked simultaneously or sequentially. In the sequential-move game, the final attack is closer to the low-valued target than it is in the simultaneous-move game. In addition, the defender chooses to defend only the location that is attacked first in the sequential game. Results from the model also can shed light on less provocative criminal events such as bank robberies and drug dealings.

Choosing an online retail channel for a manufacturer: Direct sales or consignment?

We analyze a manufacturer's e-channel decision problem in which the manufacturer selects a direct-sales channel or a third-party consignment channel to complement his existing physical retail channel. We accordingly investigate two possible dual channels: a PD system involving a physical channel and a direct e-channel, and a PC system consisting of a physical channel and a consignment e-channel. For each system, we examine both a sequential-move game and a simultaneous-move game, as the manufacturer can strategically decide to announce his pricing decision before the physical retailer or to make his pricing decision with no communication with the physical retailer. Our analytical results indicate that, if the manufacturer's unit operating cost in the direct e-channel or the e-tailer's revenue allocation ratio in the consignment e-channel is sufficiently small, then the manufacturer has an incentive to adopt an e-channel. The manufacturer can always gain a higher profit by announcing his pricing decision before the physical retailer. If the manufacturer aims at increasing the demand, then he may choose the simultaneous-move game. Moreover, when the manufacturer selects an e-channel to increase his profit, he should adopt a direct e-channel if his unit e-channel operating cost is below a certain threshold that is dependent on the e-tailer's revenue allocation ratio, and adopt a consignment e-channel otherwise. A similar managerial insight is drawn when the manufacturer intends to increase the demand.