Theory of dynamic processes with several competing actors that try to achieve some goal in a strategic way.
3
votes
0answers
52 views
Game Theory: Regret Minimization
I try to get some intuition behind regret minimization in game theory by reading Learning, Regret minimization, and Equilibria by A. Blum and Y. Mansour.
The main problem is I am sort of confused by ...
1
vote
0answers
92 views
Toads and frogs game algorithm
I am looking for an algorithm (or hint where to start), for Toads and Frogs Game. What I am interested in is not how to solve the problem (it's NP-hard), but how to plan one player's moves. I.e. how ...
1
vote
0answers
49 views
Tools for mathematical modelling in Game theory
I am looking for tools(/softwares) which will help in doing mathematical modelling for Game theoretic models. The ones which I know of are Gambit and QtxGame. But I need something which will allow me ...
3
votes
1answer
42 views
Difference between Dominant strategy and Winning Strategy
I am a little bit confused by the definition of dominant strategy and winning strategy, what's the difference between them.
Following are the definitions taken from wikipedia, below every definition ...
6
votes
2answers
77 views
Fair cake-cutting when players join late
The usual statement of the fair cake-cutting problem assumes that all $n$ players get their share at the same time. However, in many cases the players arrive incrementally. For example, we may divide ...
2
votes
0answers
36 views
Fair division of two-dimensional cake
I am interested in procedures for fair division of land (i.e. envy-free division, or at least proportional division).
In contrast to the well-studied cake-division problem, land-division is ...
2
votes
1answer
87 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 ...
1
vote
3answers
52 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 ...
3
votes
1answer
58 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 ...
9
votes
0answers
170 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 ...
2
votes
0answers
37 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 ...
6
votes
2answers
173 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 ...
0
votes
1answer
428 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 ...
1
vote
1answer
97 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 ...
5
votes
1answer
119 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 ...
6
votes
1answer
136 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
votes
1answer
91 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.
7
votes
1answer
168 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 ...
