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Volume 6, 2019

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Journal of Dynamics & Games

July 2019 , Volume 6 , Issue 3

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Free mobility of capital and Labor force in a two-country model: The dynamic game for growth
Elvio Accinelli, Edgar Sánchez Carrera, Laura Policardo and Osvaldo Salas
2019, 6(3): 179-194 doi: 10.3934/jdg.2019013 +[Abstract](541) +[HTML](285) +[PDF](399.64KB)
Abstract:

In this paper, we consider a two-country and two-sector economy, where firms can choose to be innovative or not innovative, and workers to be skilled or unskilled. Using a dynamic game, we argue that exploiting the comparative advantages a country has in producing goods that use the most abundant factor of production, free mobility of capital and labor is beneficial for economic growth. However, if a country has a comparative advantage in a sector that uses intensely unskilled labor (which is the case of several underdeveloped economies), a poverty trap may arise. For this reason we argue that national Governments must ensure the technological development to improve competitiveness and therefore a social optimal use of the comparative advantages.

Cooperative dynamic advertising via state-dependent payoff weights
Simon Hoof
2019, 6(3): 195-209 doi: 10.3934/jdg.2019014 +[Abstract](369) +[HTML](171) +[PDF](510.99KB)
Abstract:

We consider an infinite horizon cooperative advertising differential game with nontransferable utility (NTU). The values of each firm are parametrized by a common discount rate and advertising costs. First we characterize the set of efficient solutions with a constant payoff weight. We show that there does not exist a constant weight that supports an agreeable cooperative solution. Then we consider a linear state-dependent payoff weight and derive an agreeable cooperative solution for a restricted parameter space.

Social networks and global transactions
Yuki Kumagai
2019, 6(3): 211-219 doi: 10.3934/jdg.2019015 +[Abstract](135) +[HTML](60) +[PDF](300.02KB)
Abstract:

In the repeated prisoner's dilemma with private monitoring, Bhaskar and Obara [2] construct a belief-based mixed trigger strategy which may be modified to approximate full cooperation when a public randomisation device is available. By modifying their assumption about trading relationships, this paper generalises the model and demonstrates that without introducing public randomisations, long-run cooperation may be approximately sustained by mixed trigger strategies with delayed communication. By applying our model, we investigate when efficient trade is attainable in a nonmarket trading system of social networks by looking into a role of communication in long-run community enforcement of efficient trade.

Discrete mean field games: Existence of equilibria and convergence
Josu Doncel, Nicolas Gast and Bruno Gaujal
2019, 6(3): 221-239 doi: 10.3934/jdg.2019016 +[Abstract](392) +[HTML](186) +[PDF](434.27KB)
Abstract:

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite time horizons. We prove the existence of a mean field equilibrium assuming continuity of the cost and of the drift. These conditions are more general than the existing papers studying finite state space mean field games. Besides, we also study the convergence of the equilibria of N -player games to mean field equilibria in our four settings. On the one hand, we define a class of strategies in which any sequence of equilibria of the finite games converges weakly to a mean field equilibrium when the number of players goes to infinity. On the other hand, we exhibit equilibria outside this class that do not converge to mean field equilibria and for which the value of the game does not converge. In discrete time this non- convergence phenomenon implies that the Folk theorem does not scale to the mean field limit.

Spatial competitive games with disingenuously delayed positions
Marzieh Soltanolkottabi, David Ben-Arieh and John (C-W) Wu
2019, 6(3): 241-257 doi: 10.3934/jdg.2019017 +[Abstract](132) +[HTML](90) +[PDF](1049.21KB)
Abstract:

During the last decades, spatial games have received great attention from researchers showing the behavior of populations of players over time in a spatial structure. One of the main factors which can greatly affect the behavior of such populations is the updating scheme used to apprise new strategies of players. Synchronous updating is the most common updating strategy in which all players update their strategy at the same time. In order to be able to describe the behavior of populations more realistically several asynchronous updating schemes have been proposed. Asynchronous game does not use a universal clock and players can update their strategy at different time steps during the play.

In this paper, we introduce a new type of asynchronous strategy updating in which some of the players hide their updated strategy from their neighbors for several time steps. It is shown that this behavior can change the behavior of populations but does not necessarily lead to a higher payoff for the dishonest players. The paper also shows that with dishonest players, the average payoff of players is less than what they think they get, while they are not aware of their neighbors' true strategy.

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