Marketing Resource Allocation Strategy Optimization Based on Dynamic Game Model

Game theory has become an important tool to study the competition between oligopolistic enterprises. After combing the existing literature, it is found that there is no research combining two-stage game and nonlinear dynamics to analyze the competition between enterprises for advertising. Therefore, this paper establishes a two-stage game model to discuss the effect of the degree of firms’ advertising input on their profits. And the complexity of the system is analyzed using nonlinear dynamics. This paper analyzes and studies the dynamic game for two types of application network models: data transmission model and transportation network model. Under the time-gap ALOHA protocol, the noncooperative behavior of the insiders in the dynamic data transmission stochastic game is examined as well as the cooperative behavior. In this paper, the existence of Nash equilibrium and its solution algorithm are proved in the noncooperative case, and the “subgame consistency” of the cooperative solution (Shapley value) is discussed in the cooperative case, and the cooperative solution satisfying the subgame consistency is obtained by constructing the “allocation compensation procedure.” The cooperative solution is obtained by constructing the “allocation compensation procedure” to satisfy the subgame consistency. In this paper, we propose to classify the packets transmitted by the source nodes, and by changing the strategy of the source nodes at the states with different kinds of packets, we find that the equilibrium payment of the insider increases in the noncooperative game with the addition of the “wait” strategy. In the transportation dynamic network model, the problem of passenger flow distribution and the selection of service parameters of transportation companies are also studied, and a two-stage game theoretical model is proposed to solve the equilibrium price and optimal parameters under Wardrop’s criterion.

Competition and Innovation in Markets with Technology Leaders

In this article, we consider technology leaders (which are innovators) and technology followers (which are non-innovators) to provide a new theoretical explanation for the well-cited empirical evidence of an inverted-U relationship between competition and aggregate innovation. We consider a two-stage game with a deterministic Research and Development (R&D) process, where the leaders first determine their R&D investments simultaneously and then all leaders and followers determine their outputs simultaneously. We show that the inverted-U relationship between competition and aggregate innovation occurs if competition is affected by the number of technology followers. However, the presence of more technology leaders decreases individual R&D investments while increasing aggregate R&D investments. If the total number of firms remains the same but the composition of technology leaders and followers changes in favor of leaders (followers), individual R&D investments decrease (increase) but aggregate R&D investments increase (decrease). The relationship between competition and R&D investments can be U-shaped if the intensity of competition is measured by product substitutability. Contrary to the standard expectation, the presence of more firms may reduce welfare.

A Novel Two-Stage Game Model for Pricing Cloud/Fog Computing Resource in Blockchain Systems

Cloud/fog computing resource pricing is a new paradigm in the blockchain mining scheme, as the participants would like to purchase the cloud/fog computing resource to speed up their mining processes. In this paper, we propose a novel two-stage game to study the optimal price-based cloud/fog computing resource management, in which the cloud/fog computing resource provider (CFP) is the leader, setting the resource price in Stage I, and the mining pools act as the followers to decide their demands of the resource in Stage II. Since mining pools are bounded rational in practice, we model the dynamic interactions among them by an evolutionary game in Stage II, in which each pool pursues its evolutionary stable demand based on the observed price, through continuous learning and adjustments. Backward induction method is applied to analyze the sub-game equilibrium in each stage. Specifically in Stage II, we first build a general study framework for the evolutionary game model, and then provide a detailed theoretical analysis for a two-pool case to characterize the conditions for the existence of different evolutionary stable solutions. Referring to the real world, we conduct a series of numerical experiments, whose results validate our theoretical findings for the case of two mining pools. Additionally, the impacts from the size of mining block, the unit transaction fee and the price of token on the decision makings of participants are also discussed.

Independent Research and Development or Technology Mergers and Acquisitions? Decision Mechanisms of Research and Development Strategies in a Two-Stage Game

This research introduces the three variables of spillover effect, research and development efficiency, and cost of mergers and acquisitions as the chief factors affecting independent research and development and technology mergers and acquisitions based on a two-stage game theory model of research and development strategies. Using these three variables, this research explains the selection of independent research and development or technology mergers and acquisitions according to profit maximization. Based on the theory model, this research finds that costs of mergers and acquisitions and spillover effects play a significant role in research and development decisions. In addition, excessive costs of mergers and acquisitions can increase research and development expenditures, therefore reducing profit and affecting the organizational operation and development. Therefore, when the costs of mergers and acquisitions exceed a certain level, companies will abandon technology mergers and acquisitions and choose independent research and development; and a higher knowledge spillover effect reduces the costs of independent research and development, therefore increasing profit. In conclusion, given certain costs of mergers and acquisitions, a higher spillover effect helps business organizations to choose independent research and development strategies.

Equilibrium payoffs in two-player discounted OLG games

This paper studies payoffs in subgame perfect equilibria of two-player discounted overlapping generations games with perfect monitoring. Assuming that mixed strategies are observable and a public randomization device is available, it is shown that sufficiently patient players can obtain any payoffs in the interior of the smallest rectangle containing the feasible and strictly individually rational payoffs of the stage game, when we first choose the rate of discount and then choose the players’ lifespan. Unlike repeated games without overlapping generations, obtaining payoffs outside the feasible set of the stage game does not require unequal discounting.

Reactive Strategies: An Inch of Memory, a Mile of Equilibria

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash Equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

Network Formation with Asymmetric Players and Chance Moves

We propose a model of network formation as a two-stage game with chance moves and players of various types. First, the leader suggests a connected communication network for the players to join. Second, nature selects a type vector for players based on the given probability distribution, and each player decides whether or not to join the network keeping in mind only his own type and the leader’s type. The game is of incomplete information since each player has only a belief over the payoff functions of others. As a result, the network is formed, and each player gets a payoff related to both the network structure and his type. We prove the existence of the Bayesian equilibrium and propose a new definition of the stable partially Bayesian equilibrium defining the network to be formed and prove its existence. The connection between the stable partially Bayesian equilibrium and the Nash equilibrium in the game is examined. Finally, we investigate the characteristics of the network structures under the stable partially Bayesian equilibrium in a three-player game with the major player as well as in the n-player game with a specific characteristic function.