18.3 : Player and Strategies

In game theory, players are individuals or groups whose decisions affect their own outcomes and the outcomes of others. For example, in a political election, candidates make decisions about campaign strategies, influencing voter support, and ultimately determining the election outcome. Each player typically has their own objectives, which they seek to achieve through strategic decision-making. The success of a player depends not only on their own decisions but also on anticipating and responding to the strategies of others. This interdependence makes understanding players' goals and predicting their actions critical in analyzing strategic scenarios.

A strategy is a plan a player follows to achieve the best possible result, which is often defined as the outcome that maximizes the player's utility or benefit. Strategy guides how the player acts in different situations, often considering what they expect others to do. There are two types of strategies: pure and mixed.

In a pure strategy, the player makes a specific choice every time. For example, a restaurant might always choose to offer free delivery to attract more customers, regardless of the actions of nearby competitors.

Mixed strategies introduce an element of unpredictability by assigning probabilities to different actions. This uncertainty prevents other players from easily predicting the next move. For instance, an online store might offer free shipping 50% of the time and charge the other 50%, depending on customer demand patterns or stock availability. This approach keeps competitors uncertain and makes it more difficult for them to respond consistently with countermeasures.

Both pure and mixed strategies offer ways for players to optimize their decisions, depending on the nature of the game and the anticipated actions of others. Pure strategies provide consistency, while mixed strategies introduce flexibility, helping players navigate uncertain or competitive environments more effectively.