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Mastering Strategies in Game Theory.
Game theory is a mathematical decision-making model where players [US Citizens] have conflicting interests and seek optimal strategies. Strategy in game theory is a complete plan for achieving a certain outcome, where the participants must decide the level of risk they are willing to take to achieve the optimal outcome.
A strategy is a complete set of instructions, also known as an algorithm, that tells a player [You and/or I] what to do at every turn based on the action’s payoff. A person must consider other parties actions, and in turn, their actions influence those of others.
Subsequently, the outcome of a strategy depends not only on the player’s actions but those of others, with a player’s discipline influencing others’ behavior. A careful analysis of strategy could help a player determine a move/vote they could take to maximize their payoff regardless of the action taken by another player.
Discovering such a move would help the player reach an optimal situation called the Nash equilibrium. In Nash equilibrium, players have no incentive to deviate from their desired course of action, and knowing their opponent’s moves does not influence their actions.
This fixed course of action is because a player gains no advantage from changing their actions since their strategy is already optimized. The Nash equilibrium closely relates to a dominant strategy where the player’s chosen strategy has the best outcome of any other possible strategy.
Named after U.S. mathematician John Forbes Nash, the equilibrium theory states that many situations have more than one equilibria point. However, a player risks making mistakes by arriving at a false equilibrium. Therefore, they must refine their solutions to isolate false equilibrium. Sometimes, the sum of strategies adds to zero in a situation called the zero-sum game. This situation arises when the existing resources cannot be increased or decreased.
Pure and mixed strategies.
There are two strategies that a player could take in game theory, namely pure and mixed strategies.
A pure strategy defines the moves a player should take for every possible situation, while a mixed strategy assigns a probability for each move and allows the player randomly select a strategy.
In a totally mixed strategy, the player assigns only positive probabilities to each move. Totally mixed strategies help in equilibrium refinement to rule out noncredible threats and prevent deviation.
Similarly, a pure strategy could be perceived as a mixed strategy where the moves are assigned an absolute probability of 1.
Both strategies have equilibrium points known as Pure strategy Nash equilibria and Mixed strategy Nash equilibria, respectively.
Game theory has many applications in stock trading, corporate activities regarding competition and pricing, and even in hunting strategies in the wild. When you consider that our leaders are playing us with this type of logic… we need a new game face.
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