Consider the two-person Stag Hunt game.First, find each player’s best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria. ### The Stag Hunt GameThe Stag Hunt game is a classic example used in game theory to illustrate coordination games with two players. Here is an explanation of the game and how to analyze it:#### Game DescriptionIn this game, we have two players and they have two strategies to choose from: hunting a stag or hunting a hare. The payoffs for each strategy combination are provided in the table below:| Payoffs | Stag | Hare ||---------|---------|---------|| **Stag**| 3, 3 | 0, 1 || **Hare**| 1, 0 | 1, 1 |- If both players choose to hunt the stag, they each receive a payoff of 3.- If one chooses stag and the other chooses hare, the stag hunter receives 0 and the hare hunter receives 1.- If both choose to hunt the hare, they each receive a payoff of 1.#### Finding Nash EquilibriaTo find the Nash equilibria, consider each player’s best response given the other player’s choice:1. **Pure Strategies:** - **(Stag, Stag):** Both players choosing Stag is a Nash equilibrium because neither player can benefit from unilaterally changing their strategy. - **(Hare, Hare):** Both players choosing Hare is also a Nash equilibrium because no player benefits from deviating alone.2. **Mixed Strategies:** - Since the payoffs for hare are less than the payout for stag if both cooperate, the mixed-strategy equilibrium involves complex calculations beyond elementary setups as pure strategies offer guaranteed beneficial outcomes over the hare play. This game setup often emphasizes the contrast between safety (Hare, Hare) and cooperation for higher gain (Stag, Stag).The Stag Hunt thus emphasizes the importance of trust and coordination to achieve the mutually most beneficial outcome.

A mixed strategy Nash equilibrium includes something like one player playing a randomized strategy…

Consider the two-person Stag Hunt game. First, find each player's best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria. payoffs Stag | Hare 3, 3 1, 0 0, 1 1, 1 Stag Hare

Consider the two-person Stag Hunt game. First, find each player's best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria. payoffs Stag | Hare 3, 3 1, 0 0, 1 1, 1 Stag Hare

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Chapter1: Making Economics Decisions

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Consider the two-person Stag Hunt game.

First, find each player’s best response functions; then plot the best response functions and find all Nash equilibria, including both pure-strategy and mixed-strategy equilibria.

### The Stag Hunt Game

The Stag Hunt game is a classic example used in game theory to illustrate coordination games with two players. Here is an explanation of the game and how to analyze it:

#### Game Description

In this game, we have two players and they have two strategies to choose from: hunting a stag or hunting a hare. The payoffs for each strategy combination are provided in the table below:

| Payoffs | Stag | Hare |
|---------|---------|---------|
| **Stag**| 3, 3 | 0, 1 |
| **Hare**| 1, 0 | 1, 1 |

- If both players choose to hunt the stag, they each receive a payoff of 3.
- If one chooses stag and the other chooses hare, the stag hunter receives 0 and the hare hunter receives 1.
- If both choose to hunt the hare, they each receive a payoff of 1.

#### Finding Nash Equilibria

To find the Nash equilibria, consider each player’s best response given the other player’s choice:

1. **Pure Strategies:**
- **(Stag, Stag):** Both players choosing Stag is a Nash equilibrium because neither player can benefit from unilaterally changing their strategy.
- **(Hare, Hare):** Both players choosing Hare is also a Nash equilibrium because no player benefits from deviating alone.

2. **Mixed Strategies:**
- Since the payoffs for hare are less than the payout for stag if both cooperate, the mixed-strategy equilibrium involves complex calculations beyond elementary setups as pure strategies offer guaranteed beneficial outcomes over the hare play. This game setup often emphasizes the contrast between safety (Hare, Hare) and cooperation for higher gain (Stag, Stag).

The Stag Hunt thus emphasizes the importance of trust and coordination to achieve the mutually most beneficial outcome.

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