This paper introduces and analyzes a binary game to study the emergence of cooperation and organization in an evolutionary game. The game involves N players choosing between two sides, with those on the minority side winning. Players use a finite set of strategies based on past records, with limited analytical power. The game highlights cooperation and competition patterns, responsive to payoff functions. Traditional economic theories are deductive, assuming rational decision-making, but recent studies suggest that real-world decisions are inductive. Evolutionary games have been studied, but new approaches are needed to account for irrationality. Bounded rationality, as proposed by B. Arthur, is a promising approach. The game involves N players with a finite number of strategies. At each step, players choose sides, and the minority side wins. Players use past records to decide their actions, with limited memory. The game's outcome depends on the strategies used, with more complex strategies leading to better performance. The game is simulated for large populations, showing that players with larger memory (more bits) perform better. However, beyond a certain point, performance plateaus. The game is symmetrical for A and B, and players face competition for minority status. The game also shows that players can spontaneously cooperate, even though they are selfish. The study also explores the effects of different strategies and memory sizes. Players with more strategies tend to perform worse, as they may switch strategies too frequently. The game includes a genetic approach, where the worst players are replaced by new ones, leading to better performance over time. The study concludes that the game provides insights into economic behavior, highlighting the need for a general approach to study evolutionary games. The game's results suggest that cooperation and organization can emerge spontaneously, even in the absence of enforceable authority. The study also suggests that the game can be extended to more complex scenarios, such as neural networks, to better understand real-world dynamics.This paper introduces and analyzes a binary game to study the emergence of cooperation and organization in an evolutionary game. The game involves N players choosing between two sides, with those on the minority side winning. Players use a finite set of strategies based on past records, with limited analytical power. The game highlights cooperation and competition patterns, responsive to payoff functions. Traditional economic theories are deductive, assuming rational decision-making, but recent studies suggest that real-world decisions are inductive. Evolutionary games have been studied, but new approaches are needed to account for irrationality. Bounded rationality, as proposed by B. Arthur, is a promising approach. The game involves N players with a finite number of strategies. At each step, players choose sides, and the minority side wins. Players use past records to decide their actions, with limited memory. The game's outcome depends on the strategies used, with more complex strategies leading to better performance. The game is simulated for large populations, showing that players with larger memory (more bits) perform better. However, beyond a certain point, performance plateaus. The game is symmetrical for A and B, and players face competition for minority status. The game also shows that players can spontaneously cooperate, even though they are selfish. The study also explores the effects of different strategies and memory sizes. Players with more strategies tend to perform worse, as they may switch strategies too frequently. The game includes a genetic approach, where the worst players are replaced by new ones, leading to better performance over time. The study concludes that the game provides insights into economic behavior, highlighting the need for a general approach to study evolutionary games. The game's results suggest that cooperation and organization can emerge spontaneously, even in the absence of enforceable authority. The study also suggests that the game can be extended to more complex scenarios, such as neural networks, to better understand real-world dynamics.