The goal of thispaper is to establish a general framework for “Consensus Game” thatcharacterizes the behavior of blockchain ecosystems, and to addressbehaviors of the “Mining Pool Gap Game”, that is, we first give thecharacterizing and interpreting the behavior of “ConsensusEquilibria”, and establishing and explaining the stability of theblockchain platform itself with the positive answer based on theexistence of consensus equilibrium through the new concept called“consensus game” in the presence of mining gap (game) behavior, here, the blockchain ecosystem where “Gap Game” is located refersto a mining platform based on the consensus principle of “Proof ofWork” (PoW) with longest chain rules (LCR) proposed by Nakamoto in2008. Specifically, this paper first establishes the existence ofgeneral consensus equilibrium and the corresponding stabilityresults for continuous operation of the blockchain ecosystem undergeneral incentive mechanism conditions, based on the consensus gameframework in the blockchain ecosystem. Then, combined with the threemain factors involved in “mining Bitcoin” work, including workcosts, reward mechanisms, and mining capabilities, from theperspective of mining miner (group) profits, it interprets andanalyzes the potential impact of different embedding scenarios onthe “gap game behavior” of mining miners (groups). The theoreticalresults and case analysis of this article indicate that by combiningappropriate incentive compatibility mechanisms for different miningscenarios, the concept of consensus game (equilibrium) can obtain orform a consistent explanation and interpretation of mining behaviorin different scenarios without simulation results of scenario data.In addition, we have reason to expect and believe that consensusgames, combined with factors related to mining (group) profits, canhelp us build appropriate incentive compatibility mechanisms. Bycharacterizing behaviors such as “interval behavior”, “branchingchains”, and “mining pool attacks”, we can support the healthydevelopment of the digital economy and promote the development ofbasic theories of consensus economics.
Population game theory is a new direction of game theory, developed in recent thirty years, which originated from "Mass-Action" interpretation on mixed strategies and equilibria in 1950 by J. Nash in his PhD dissertation. It established rational decision making theory for individuals in population and society consisting of large number of individuals, and has been applied extensively and intensively in sociology, biology, economics, management science and information science, etc. In this paper, we give a review on recent advances of population game theory and investigate new developing directions.
With differential games and classical pursuit-evasion problems as the main focus, this article aims to trace the historical development of group pursuit-evasion differential games. By addressing large-scale group pursuit-evasion issues from the point of mean-field games, the prospects of applying reinforcement learning techniques are elucidated. It proposes exploring solutions to inverse pursuit-evasion differential games, suitable for scenarios such as underwater autonomous vessels, terrestrial robots, and swarms of unmanned aerial vehicles. Diverging from other review papers, it devotes significant attention to the distinctive academic schools of thought in Russia and the former Soviet Union, highlighting their influence in the evolution of this field.
With the increasing integration of global economy and closer international relations, win-win cooperation has become a core trend in today. As a powerful tool for studying cooperative issues, cooperative game mainly explores how to allocate the benefits generated by cooperation among players. The Shapley value, as one of the most important solutions in cooperative games, has significant research significance and value. This paper mainly introduce some research on the axiomatization of the Shapley value from the point of additivity, balanced contribution, marginality, fairness, reduced consistency, associated consistency and some special player properties. We finally give a brief summary from the perspective of future research.
Pooling, unpooling/specialization, and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare, call centers, and online sales. These strategies may have advantages and disadvantages in different operational environments. This paper uses the $M/M/1$ and $M/M/2$ queues to study the impact of pooling, specialization, and discretionary task completion on the average queue length. Closed-form solutions for the average $M/M/2$ queue length are derived. Computational examples illustrate how the average queue length changes with the strength of pooling, specialization, and discretionary task completion. Finally, several conjectures are made in the paper.
A model of continuous-time insider trading in which a risk-neutral insider possesses two imperfect correlated signals of a risky asset is studied. By conditional expectation theory and filtering theory, we first establish three lemmas: normal correlation, equivalent pricing and equivalent profit, which can guarantee to turn our model into a model with insider knowing full information. Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule. It shows that in the equilibrium, (1) the market depth is constant over time; (2) if the two noisy signals are not linerly correlated, then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end; (3) if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value, then our model turns into a model with insider knowing full information; (4) if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing, while down to 0 as the noise going up to infinity; (5) if the two noisy signals are not linear correlated then with one noisy signal fixed, the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value, and furthermore as the noisy value going to 0 it gets its maximum, the profit in the case that the real value is observed.
The wind power industry is rapidly developing under the '3060' dual-carbon strategy. Preventive maintenance has become crucial in improving the operational reliability of wind turbines. However, operational management of wind turbines in complex environments still lacks sufficient understanding of the degradation state and reliable maintenance strategies. This paper examines the relationship between the degradation process of wind turbine key components and a multi-stage preventive maintenance strategy. The objective is to minimize expected costs. Based on Markov degraded state transfer, a multi-stage preventive maintenance cost model is constructed. This paper describes a model that utilizes the equipment decline law and Markov chain to portray the degraded state and maintenance strategy. It also introduces reliability, failure rate, and service age factors to calculate multi-stage preventive maintenance and failure hours. Additionally, the model considers the influence of weather conditions on the maintenance cost of wind turbines throughout the maintenance cycle. Numerical simulation is used to solve and analyze the model. The results indicate that the minimum and replacement maintenance strategy accounts for over 80% of the total maintenance cost, while the preventive maintenance optimization strategy accounts for less than 20%. Therefore, wind power enterprises in low wind speed areas can use this strategy as a practical reference for decision-making to enhance the operational reliability of wind turbines.
How to determine fair and reasonable allocation schemes (i.e. solutions of the game) is an important research content of cooperative games. The marginal distribution principle based on the contribution of players and the social distribution principle considering the internal connections of players are widely used in the definition of solutions. Various combination solutions usually reflect both types of these two distribution principles. In response to the problem of exogeneity and lack of reasonable explanation of combination parameters in existing combination solutions, this paper utilizes the social acceptability of solutions to mainly analyze two types of combination solutions based on Shapley value, Solidarity value, ENSC value, and equal division value. Sufficient (necessary) conditions for selecting parameter range in combination solutions are given, and the relationship between different social acceptability is elucidated. Furthermore, we reveal the impact of combination coefficients on the behavior of players.
The refinement and formalization of equilibrium concepts mark the establishment of game theory as a distinct discipline. The development of game theory has been centered around the fundamental properties of various equilibrium concepts. It is generally accepted that the nonexistence of equilibrium is seen as a negative outcome, impeding the advancement of equilibrium research. This holds true for economic research as well. This paper illustrates, through two examples from the literature on non-cooperative games and perfectly competitive markets, that sometimes valuable interpretations can be provided for the nonexistence of equilibrium. The first example examines the evolution of fashion phenomena through a network game based on matching pennies, where the nonexistence of equilibrium is used to interpret the emergence of fashion cycles. The second example discusses the matching problem between companies and workers in a perfectly competitive labor market, where the nonexistence of equilibrium is used to explain the phenomenon of early contracting. Additionally, we briefly introduce Shapley's insightful interpretation regarding the empty core in transferable utility cooperative games.
In this paper, we study the strong Nash equilibria of games with additively coupled utilities and a continuum of players. We first prove the existence of strong Nash equilibria for games with additively coupled utilities and finitely many players. Furthermore, we introduce the notion of weak strong Nash equilibria for games with additively coupled utilities and a continuum of players, and prove the existence theorem. Our paper develops the work of strong Nash equilibria.
This studies the existence and stability of α-core of games with discontinuous vector payoffs. By proposing the conditions of minimum values of games with vector payoffs and coalitional C-security, this gives two kinds of sufficient conditions to guarantee the existence of α-core of games with discontinuous vector payoffs. Furthermore, by using the lemma for generalized Hadmard well-posedness, the well-posedness of α-core is proven for a kind of game with discontinuous vector payoffs.
