Game Theory

What role does strategic moves play in pay-offs?

Strategic moves play a significant role in influencing game outcomes by allowing players to alter the incentives and payoffs in a way that benefits them. These moves, as defined by Thomas Schelling, are actions taken early in a game to favorably influence the ultimate outcome.

Here's a breakdown of how strategic moves impact game outcomes, based on the sources:

• Altering Payoffs: Strategic moves aim to change the payoffs of a game to shift the outcome in favor of the player making the move. This can involve side payments, promises, or threats.

• Side Payments: Players can use side payments (a type of bribe) to incentivize an opponent to choose a strategy that is in the player's best interest.

  • For example, a player might offer a payment to an opponent conditional on the opponent choosing a specific action.

  • Interestingly, just having the ability to make side payments can sometimes work, even if no money actually changes hands.

• Commitment: To gain first-mover advantage, a firm needs to make a credible commitment, which involves choices (or restricting choices) that guarantee that a player will take a particular future action should certain conditions occur that transform the game.

• Credible Commitments: A key aspect of strategic moves is credibility. A firm needs to take actions ahead of time that would make it costly for it not to follow through on its threat and thus signal to the firm's opponent that the firm will carry out its threat.

  • A firm can make a noncredible threat, but this will not influence the other player.

• Reputation: Establishing a reputation can deter the entry of a rival.

  • A firm can benefit from establishing a reputation for aggressively fighting any entry in any market. This might mean incurring costs (even though doing so could harm its current profit) to promote its reputation as a fighter to deter future entrants.

• Entry Deterrence: Preventing market entry can lead to higher profits for firms. To effectively deter entry, an incumbent firm needs to make its threat to fight credible.

• Strategic use of overcapacity is one way to affect the game's payoffs in an advantageous way.

In essence, strategic moves are proactive steps taken by players to shape the game's landscape, influence their opponents' decisions, and ultimately secure a more favorable outcome for themselves.

How does credible commitments change game structure?

Credible commitments significantly alter game structure by changing the incentives and payoffs, thereby influencing the decisions of other players. A credible commitment is a choice, or a restriction of choices, that guarantees a player will take a particular future action if certain conditions occur, effectively transforming the game.

Here's how credible commitments affect game structure:

• Altering the Payoff Matrix: Credible commitments can alter a player's payoffs, making certain actions more or less attractive. For example, Warner Brothers made a commitment that would cost it $151 million if The LEGO Movie 2 opens in December. Subtracting 151 from Warner Brothers' payoffs in the "December" row changes its payoffs to 49 in the lower left and -151 in the lower right. Now, no matter what Disney does, Warner Brothers is better off if it chooses May.

• Creating a Dominant Strategy: When a credible commitment changes the payoffs enough, it can turn a previously non-dominant strategy into a dominant strategy.

  • If Warner Brothers makes commitments that will cost it $151 million if The LEGO Movie 2 opens in December, then opening in May will become a dominant strategy for Warner Brothers.

• Influencing Opponent's Behavior: By making a credible commitment, a player can credibly signal its intentions, influencing its opponent's subsequent actions.

  • Once Warner Brothers has made its threat to open in May credible, Disney's best response is to choose a December release date.

• Deterring Entry: Credible commitments are frequently used to deter entry into a market.

  • For instance, an incumbent firm can invest in excess capacity to signal its willingness to engage in a price war if a new firm enters the market.

  • If Apple invests in extra capacity at an earlier date, and this investment lowers its profit to $1.2 billion in the monopoly case with no entry (because the extra factory capacity sits idle) and to $0.6 billion if Samsung enters and Apple chooses not to fight, this would change the game tree because Apple's threat to fight is now credible.

• Shaping Future Interactions: A credible commitment today shapes future interactions by limiting a player's future flexibility and altering the strategic landscape.

  • By making a December choice so unappealing as to be impossible, Warner Brothers effectively commits itself to take its threatened action (opening in May).

A key distinction is that of credible versus non-credible threats. A noncredible threat is a threat that a player would not rationally carry out. A firm not only needs to threaten to open in May, it also needs to take actions ahead of time that would make it costly for it to not do so and thus signal to the firm's opponent that the firm will carry out its threat.

What role does strategic moves play in pay-offs?

Strategic moves play a significant role in influencing game outcomes by allowing players to alter the incentives and payoffs in a way that benefits them. These moves, as defined by Thomas Schelling, are actions taken early in a game to favorably influence the ultimate outcome.

Here's a breakdown of how strategic moves impact game outcomes, based on the sources:

• Altering Payoffs: Strategic moves aim to change the payoffs of a game to shift the outcome in favor of the player making the move. This can involve side payments, promises, or threats.

• Side Payments: Players can use side payments (a type of bribe) to incentivize an opponent to choose a strategy that is in the player's best interest.

  • For example, a player might offer a payment to an opponent conditional on the opponent choosing a specific action.

  • Interestingly, just having the ability to make side payments can sometimes work, even if no money actually changes hands.

• Commitment: To gain first-mover advantage, a firm needs to make a credible commitment, which involves choices (or restricting choices) that guarantee that a player will take a particular future action should certain conditions occur that transform the game.

• Credible Commitments: A key aspect of strategic moves is credibility. A firm needs to take actions ahead of time that would make it costly for it not to follow through on its threat and thus signal to the firm's opponent that the firm will carry out its threat.

  • A firm can make a noncredible threat, but this will not influence the other player.

• Reputation: Establishing a reputation can deter the entry of a rival.

  • A firm can benefit from establishing a reputation for aggressively fighting any entry in any market. This might mean incurring costs (even though doing so could harm its current profit) to promote its reputation as a fighter to deter future entrants.

• Entry Deterrence: Preventing market entry can lead to higher profits for firms. To effectively deter entry, an incumbent firm needs to make its threat to fight credible.

• Strategic use of overcapacity is one way to affect the game's payoffs in an advantageous way.

In essence, strategic moves are proactive steps taken by players to shape the game's landscape, influence their opponents' decisions, and ultimately secure a more favorable outcome for themselves.

How does credible commitments change game structure?

Credible commitments significantly alter game structure by changing the incentives and payoffs, thereby influencing the decisions of other players. A credible commitment is a choice, or a restriction of choices, that guarantees a player will take a particular future action if certain conditions occur, effectively transforming the game.

Here's how credible commitments affect game structure:

• Altering the Payoff Matrix: Credible commitments can alter a player's payoffs, making certain actions more or less attractive. For example, Warner Brothers made a commitment that would cost it $151 million if The LEGO Movie 2 opens in December. Subtracting 151 from Warner Brothers' payoffs in the "December" row changes its payoffs to 49 in the lower left and -151 in the lower right. Now, no matter what Disney does, Warner Brothers is better off if it chooses May.

• Creating a Dominant Strategy: When a credible commitment changes the payoffs enough, it can turn a previously non-dominant strategy into a dominant strategy.

  • If Warner Brothers makes commitments that will cost it $151 million if The LEGO Movie 2 opens in December, then opening in May will become a dominant strategy for Warner Brothers.

• Influencing Opponent's Behavior: By making a credible commitment, a player can credibly signal its intentions, influencing its opponent's subsequent actions.

  • Once Warner Brothers has made its threat to open in May credible, Disney's best response is to choose a December release date.

• Deterring Entry: Credible commitments are frequently used to deter entry into a market.

  • For instance, an incumbent firm can invest in excess capacity to signal its willingness to engage in a price war if a new firm enters the market.

  • If Apple invests in extra capacity at an earlier date, and this investment lowers its profit to $1.2 billion in the monopoly case with no entry (because the extra factory capacity sits idle) and to $0.6 billion if Samsung enters and Apple chooses not to fight, this would change the game tree because Apple's threat to fight is now credible.

• Shaping Future Interactions: A credible commitment today shapes future interactions by limiting a player's future flexibility and altering the strategic landscape.

  • By making a December choice so unappealing as to be impossible, Warner Brothers effectively commits itself to take its threatened action (opening in May).

A key distinction is that of credible versus non-credible threats. A noncredible threat is a threat that a player would not rationally carry out. A firm not only needs to threaten to open in May, it also needs to take actions ahead of time that would make it costly for it to not do so and thus signal to the firm's opponent that the firm will carry out its threat.

What differentiates pure from mixed strategies?

Pure and mixed strategies represent fundamentally different approaches to game playing, differing in the certainty with which a player chooses an action.

Here's a breakdown of the key distinctions, based on information from the sources:

• Pure Strategy:

  • Involves a player choosing a specific action with certainty.

  • The player makes a choice between different actions, picking the specific strategy that maximizes her payoff.

  • The player follows that strategy all of the time.

• Mixed Strategy:

  • Involves a player randomizing her actions.

  • The player chooses her actions randomly from the set of pure strategies available to her.

  • The randomization pattern (e.g., whether the probability mix is 80/20, 50/50, or anything else) is itself a strategy.

  • A player using a mixed strategy might choose one option some of the time and another option at other times.

  • In a mixed-strategy Nash equilibrium, both players are indifferent between the actions they randomize over.

    • Each player needs to pick the probability of taking each action so that the player's opponent is indifferent between her own actions.

In essence, a pure strategy is a deterministic approach where a player always chooses the same action, while a mixed strategy is a probabilistic approach where a player randomizes between different actions.

How can backward induction solve game theory

Backward induction is a method used in game theory to determine optimal strategies by analyzing the game's end and working backwards to the present. It involves predicting the actions of players based on their rational choices at each stage, ultimately leading to a solution that identifies the optimal moves for all players involved.