Find the Nash equilibrium in a Diner's Dilemma game:

Find a Nash equilibrium in the Battle of the Bismarck game:

Determine to which actions this corresponds:

Since an infinite number of solutions is possible, consider finding only 3 Nash equilibria:

Find the Nash equilibrium in the Rock Paper Scissors game:

This corresponds to both players randomly choosing among rock, paper and scissors:

Find Nash equilibria in the Platonia Dilemma game:

Filter to only give mixed strategies by using the "Mixed" specification:

Find the Nash equilibria in the Volunteer's Dilemma:

To obtain only the pure strategies, use the "Pure" specification:

Generate a game:

You can use the default SolveValues method:

Use the NSolveValues method:

Use the FindInstance method:

The Volunteer's Dilemma describes a situation where each player can either volunteer or defect. If at least one player volunteers, all other players marginally benefit from defecting. If no player volunteers, all players have a very low payoff. Generate a Volunteer's Dilemma game with 4 players:

The Volunteer's Dilemma has a Nash equilibrium in many cases where it is most probable exactly one player volunteers. Find the optimal game strategies in this game:

The Discoordination game is a hybrid form of coordination and anti-coordination games, where one player's incentive is to coordinate while the other player tries to avoid this. Generate a Discoordination game with a volunteer and a detractor:

Find the optimal game strategies in this game:

Find the corresponding payoffs:

Three hungry men go to a restaurant and decide to split the bill evenly. There are three meal options, Cheap, Average and Expensive. Represent this situation as a MatrixGame:

Plot the game:

Find the Nash equilibrium:

The Cournot Oligopoly game describes a situation where a group of firms produces the same good. Each firm must consider the production cost and the quantity the other firms are producing. Only the firms with the lowest price sell goods. Generate a Cournot Oligopoly game:

Find the optimal game strategies in this game:

This is intuitive when considering that for all players, the payoffs are largest for the second action:

A price war refers to a game where multiple firms have an interest in offering the lowest price, but the payoff of any firm is directly correlated to the price chosen. Consider a price war among 3 firms where each firm has the choice between a low price and a high price:

Visualize the game:

Despite the common interest of having the price as high as possible, competition creates a Nash equilibrium at the low price:

The Colonel Blotto game describes a situation where officers (players) are tasked to simultaneously distribute limited resources over several objects (battlefields). The player devoting the most resources to a battlefield wins that battlefield, and the gain (or payoff) is equal to the total number of battlefields won. Generate a Colonel Blotto game:

Find the optimal strategies in this game:

This is intuitive, considering the second player has more resources, though spreading the resources increases the probable number of battlefields where the player can win:

Rock Paper Scissors is a zero-sum game, where either one player wins and the other loses, or there is a tie. According to game theory, the Nash equilibrium strategy of Rock Paper Scissors for both players is to randomly choose among rock, paper and scissors. Find that strategy for this game:

Generalize Rock Paper Scissors to Rock Paper Scissors Fire Water by setting up dominance order using a graph:

Create the whole game as a zero sum game:

Show the dataset:

Compute the Nash equilibrium:

Consider the difference between pure coordination and dangerous coordination games:

Symmetrical games imply some symmetrical strategies are Nash equilibria. However, asymmetrical games do not imply some asymmetrical strategies are Nash equilibria. Find the optimal game strategies in this game: