# American Institute of Mathematical Sciences

July  2019, 6(3): 241-257. doi: 10.3934/jdg.2019017

## Spatial competitive games with disingenuously delayed positions

 1 Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2069 Rathbone Hall, 1701B Platt St., Manhattan, Kansas, Riley, USA 2 Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2061 Rathbone Hall, 1701A Platt St., Manhattan, Kansas, Riley, USA

Received  December 2018 Revised  May 2019 Published  July 2019

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.

Citation: Marzieh Soltanolkottabi, David Ben-Arieh, John (C-W) Wu. Spatial competitive games with disingenuously delayed positions. Journal of Dynamics & Games, 2019, 6 (3) : 241-257. doi: 10.3934/jdg.2019017
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Illustrating Hiding Strategy
Percentage of Hawks in the final lattice
Final distribution of players in the lattice in Figure 2
Average of percentage of Hawks in the final lattice for different values of $b$
Average payoff of players in the final lattice using different $b$ values
Average of payoff for various player types using different $b$ values
Percentage of Hawks using different time steps
Percentage of Hawks using different percentage of dishonest players
Percentage of Hawks for 20 different randomly generated initial lattices for $b$ equal to 3.2, 3.3, 3.4 and 3.5
Payoff matrix for chicken game
 Hawk Dove Hawk $(b-C)/2$ $b$ Dove 0 $b/2$
 Hawk Dove Hawk $(b-C)/2$ $b$ Dove 0 $b/2$
Average of percentage of Hawks in the final lattice for different values of $b$
 b value 1 3 5 7 9 Synchronous updating 0.04922 0.19522 0.27369 0.73168 1 Asynchronous updating (displayed strategy) 0.01184 0.12838 0.41834 0.82762 1 Asynchronous updating (true strategy) 0.0121 0.12589 0.42632 0.82852 1
 b value 1 3 5 7 9 Synchronous updating 0.04922 0.19522 0.27369 0.73168 1 Asynchronous updating (displayed strategy) 0.01184 0.12838 0.41834 0.82762 1 Asynchronous updating (true strategy) 0.0121 0.12589 0.42632 0.82852 1
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