Questions tagged [game-theory]

Theory of dynamic processes with several competing actors that try to achieve some goal in a strategic way.

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1answer
236 views

Poker with Bluffing (game theory)

I'm doing a self-study of Game Theory Evolving by Gintis, and am stuck on problem 4.16 "Poker with Bluffing". The first question asks "Show that Ollie has 64 pure strategies and Stan has 8 pure ...
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3answers
1k views

Is this NIM game tree correct?

I have an assignment to construct a game of Nim (a game in which two players must divide a pile of tokens into two unequal sizes; 6 can be divided into 2 & 4 but not 3 & 3). I was provided a ...
4
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1answer
71 views

Minimal-envy land division

There is a land divided to $D$ districts. There are $C$ citizens. We want to divide the land to the citizens, such that each citizen receives a single land-plot in a single district. Each citizen ...
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0answers
539 views

Complexity of deciding whether there is a winning strategy in the following game

The sum divider game for $n$ starts with the set $M_0 = \{1,\dots,n\}$. Player A chooses a number $m_1$ from $M_0 \setminus \{1\}$ and B has to choose a divider $m_2$ of $m_1$ from $M_1 = M_0 \...
4
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1answer
67 views

Congestion Game with Varying Price

I molded my problem as the following game (it is a congestion game with varying price): $N$ players share resources $E$, $S_i$ is the strategy space of player $i$ which is in $2^E$ (where $2^E$ is ...
7
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2answers
205 views

Is it more effective to vote for a woman?

A certain political party wants to encourage women to participate in their primary elections, so they decide, that the 4th position is reserved for a woman. That is, if there is no woman in the top 4 ...
2
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2answers
13k views

Nim game tree + minimax

Problem : Two players have in front of them a single pile of objects, say a stack of 7 pennies. The first player divides the original stack into two stacks that must be unequal. Each player ...
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1answer
171 views

Expected gain of a game of chance with differently-priced tokens

Foo and Bar are playing a game of strategy. At the start of the game, there are $N$ apples, placed in a row (in straight line). The apples are numbered from $1$ to $N$. Each apple has a particular ...
7
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1answer
143 views

voting scheme for peaceful coexistence

Many areas in the world suffer from conflicts between two groups (usually ethnic or religious). For the purpose of this question, I assume that most people of both sides want to live in peace, but ...
7
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1answer
652 views

Alpha-Beta Pruning with simultaneous moves?

I have a game I'm building some ai for that has 2 players making simultaneous moves. In this game there is exactly one move where, if they both make it at the same time, the outcome is different than ...
4
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1answer
258 views

Mixed-strategy Nash equilibria

Is the following statement always true: if there is a mixed-strategy Nash equilibria then it is unique. I know that there can be several pure strategy Nash equilibrias.
8
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1answer
1k views

What use are the minimum values on minimax trees?

Consider a minimax tree for an adversarial search problem. For example, in this picture (alpha-beta pruning): When marking the the tree with $[\min,\max]$ values bottom-up, we first traverse node $3$ ...

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