Complete laboratory index

All Labs

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18 labs found

Combinatorial Games

Take-Away

Learning outcome: Classify positions as winning or losing by working backward, then pick a winning move.

Level: Introductory
Time: About 15 min
Concepts: P-positions · N-positions · Backward induction

A row of five tokens from which a player removes one or two, leaving a smaller pile.

Combinatorial Games

Nim

Learning outcome: Use the binary nim-sum to decide who wins a Nim position and find a winning move.

Level: Introductory
Time: About 20 min
Concepts: Nim-sum (XOR) · Bouton's theorem · Misère play

Three piles of tokens, with two tokens being removed from the tallest pile.

Combinatorial Games

Graph Games

Learning outcome: Compute Sprague–Grundy values on a directed graph with the minimum-excluded rule.

Level: Intermediate
Time: About 20 min
Concepts: Sprague–Grundy value · mex · Followers

A directed graph of five vertices with a token on the start vertex and one highlighted move.

Combinatorial Games

Sum of Games

Learning outcome: Combine the Grundy values of independent games with XOR to play their sum.

Level: Intermediate
Time: About 20 min
Concepts: Game sums · Sprague–Grundy theorem · Nim-sum

Three piles of one, two and three tokens combined as 1 XOR 2 XOR 3 equals 0.

Combinatorial Games

Hackenbush

Learning outcome: Replace rooted Green Hackenbush branches by equivalent Nim heaps and choose a winning cut.

Level: Intermediate
Time: About 25 min
Concepts: Green Hackenbush · Colon principle · Equivalent Nim heap

A rooted Hackenbush tree standing on the ground, with blue and red edges and yellow vertices.

Strategic Games4 methods

Zero-Sum Matrix Games

Methods: Solve & Play · Linear Programming · Pivot Method · Fictitious Play

Learning outcome: Find the value and optimal mixed strategies of a zero-sum game, then reach them through linear programming, pivoting and fictitious play.

Level: Intermediate
Time: About 20 min per method
Concepts: Saddle point · Mixed strategy · Minimax theorem · Linear programming

A three by three payoff matrix with a blue row player on the left and a red column player on the top.

Strategic Games3 methods

General-Sum Games

Methods: Nash Equilibria · Safety Levels · Dominance

Learning outcome: Find the Nash equilibria of a two-player game and compare them with safety levels and dominance.

Level: Intermediate
Time: About 20 min per method
Concepts: Nash equilibrium · Best response · Safety level · Dominance

Two players facing a two by two payoff table with a payoff pair in each cell.

Strategic Games3 methods

Game Trees

Methods: Tree Builder · Backward Induction · Behavioral Strategies

Learning outcome: Build a game tree, read its information sets and solve perfect-information games by backward induction.

Level: Intermediate
Time: About 20 min per method
Concepts: Information sets · Backward induction · Behavioral strategies

A blue player on a yellow path that forks while a red player stands on one of the branches.

Strategic Games

Continuous Poker

Learning outcome: Derive betting and calling thresholds when private hands range over an interval.

Level: Advanced
Time: About 20 min
Concepts: Threshold strategy · Bluffing · Indifference

A blue player and a red player holding cards at a round blue table with a pile of chips between them.

Strategic Games

Poker Endgame

Learning outcome: Find a bluffing rate and a calling rate from indifference conditions.

Level: Intermediate
Time: About 15 min
Concepts: Hidden information · Bluffing · Indifference

A sweating, anxious faceless blue player holding a card and a chip while a red devil whispers bluff and a yellow angel whispers call.

Strategic Games

Stochastic Game

Learning outcome: Compute state values with Shapley iteration and evaluate stationary policies.

Level: Advanced
Time: About 25 min
Concepts: State value · Shapley iteration · Stationary policy

A red player and a blue player paddling a yellow canoe together through rolling blue waves.

Economic Competition

Cournot Duopoly

Learning outcome: Find each firm's best quantity and the equilibrium where the reaction curves cross.

Level: Intermediate
Time: About 20 min
Concepts: Reaction curve · Cournot equilibrium · Best response

A blue factory and a red factory sending conveyor belts of yellow cubes into one shared golden market tray.

Economic Competition

Bertrand Competition

Learning outcome: Explain why identical firms undercut prices down to cost, and how differentiation keeps prices higher.

Level: Intermediate
Time: About 20 min
Concepts: Undercutting · Bertrand equilibrium · Product differentiation

Two scenes of a blue and a red seller pricing identical mugs at $6 and $7, then differentiated mugs at $7 and $8, with a yellow buyer choosing between them.

Economic Competition

Stackelberg Competition

Learning outcome: Solve leader–follower quantity competition by backward induction and measure the first-mover advantage.

Level: Intermediate
Time: About 20 min
Concepts: Commitment · Backward induction · First-mover advantage

A blue leader at factory number one thinking about the quantity a red follower at factory number two will produce in response.

Economic Competition

Entry Deterrence

Learning outcome: Find the incumbent output at which entry stops paying and judge whether that threat is credible.

Level: Intermediate
Time: About 20 min
Concepts: Entry cost · Deterrence threshold · Commitment

A blue incumbent factory filling a golden market tray with yellow cubes while a red entrant weighs whether to build a factory, with a stack of coins beside them.

Cooperation & Coalitions3 methods

Two-Player Cooperation

Methods: Feasible Payoffs · Transferable Utility · Nash Bargaining

Learning outcome: Map the feasible agreements of two players and choose one with transferable utility or Nash bargaining.

Level: Intermediate
Time: About 20 min per method
Concepts: Feasible set · Pareto frontier · Transferable utility · Nash bargaining

A blue player and a red player shaking hands over a dark divider, with a row of yellow gold bars split between them and one bar being slid across.

Cooperation & Coalitions9 methods

Coalitional Games

Methods: Game Builder · Imputations · Core · Shapley Value · Shapley Axioms · Alternative Formula · Nucleolus · Compare Solutions · Nucleolus Exercises

Learning outcome: Compare imputations, the core, the Shapley value and the nucleolus on one characteristic function.

Level: Advanced
Time: About 20 min per method
Concepts: Characteristic function · Core · Shapley value · Nucleolus

A blue player and a red player shaking hands beside a small stack of yellow cubes while a yellow third player holds out one more cube to join them.

Cooperation & Coalitions

Voting Power

Learning outcome: Measure Shapley–Shubik power from pivotal voters and separate voting weight from power.

Level: Intermediate
Time: About 15 min
Concepts: Weighted voting · Pivotal voter · Shapley–Shubik index

A blue voter with weight 4, a yellow voter with weight 2 and a red voter with weight 3 around a round table, with a quota card reading 5 and a gold ring around the blue and yellow weights.