Strategic fair division is the branch of
fair division in which the participants are assumed to hide their preferences and act strategically in order to maximize their own utility, rather than playing sincerely according to their true preferences.
To illustrate the difference between strategic fair division and classic fair division, consider the
divide and choose procedure for dividing a cake among two agents. In classic fair division, it is assumed that the cutter cuts the cake into two pieces that are equal in his eyes, and thus he always gets a piece that he values at exactly 1/2 of the total cake value. However, if the cutter knows the chooser's preferences, he can get much more than 1/2 by acting strategically. For example, suppose the cutter values a piece by its size while the chooser values a piece by the amount of chocolate in it. So the cutter can cut the cake into two pieces with almost the same amount of chocolate, such that the smaller piece has slightly more chocolate. Then, the chooser will take the smaller piece and the cutter will win the larger piece, which may be worth much more than 1/2 (depending on how the chocolate is distributed).
The research in strategic fair division has two main branches.
One branch is related to
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
and studies the equilibria in games created by fair division algorithms:
* The
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
of the Dubins-Spanier moving-knife protocol;
* The Nash equilibrium and
subgame-perfect equilibrium
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every ...
of generalized-cut-and-choose protocols;
* The equilibria of envy-free protocols for allocating an indivisible good with monetary compensations.
*The
price of anarchy The Price of Anarchy (PoA) is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficien ...
of Nash equilibria of two mechanisms for homogeneous-resource allocation: the
Fisher market Fisher market is an economic model attributed to Irving Fisher. It has the following ingredients:
* A set of m divisible products with pre-specified supplies (usually normalized such that the supply of each good is 1).
* A set of n buyers.
* For ea ...
game and the Trading Post game.
The other branch is related to
mechanism design and aims to find
truthful mechanisms for fair division, in particular:
*
Truthful cake-cutting Truthful cake-cutting is the study of algorithms for fair cake-cutting that are also truthful mechanisms, i.e., they incentivize the participants to reveal their true valuations to the various parts of the cake.
The classic divide and choose proced ...
;
*
Truthful resource allocation Truthful resource allocation is the problem of allocating resources among agents with different valuations over the resources, such that agents are incentivized to reveal their true valuations over the resources.
Model
There are ''m'' resources t ...
;
*
Truthful fair division of rooms and rent.
References
{{Reflist
Fairness criteria
Mechanism design
Game theory