A bargaining set for roommate problems

Atay, Ata; Mauleon, Ana; Vannetelbosch, Vincent

doi:10.1016/j.jmateco.2020.102465

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…To make this precise, we say that a partition π is dominated via S if v i (S) > V i (π) for all i ∈ S. The core is the set of undominated partitions. 1 Example 2.1 (The roommate problem) There are three players who have to decide about who of them will be moving in together in a two-bedroom flat. They have somewhat conflicting interests: While everybody dislikes to move in with three people into a two-bedroom flat, 1 prefers to move in with 2 over moving in with 3 over staying alone; 2 prefers moving in with 3 over moving in with 1 over staying alone; and 3 prefers moving in with 1 over moving in with 2 over staying alone.…”

Section: Hedonic Gamesmentioning

confidence: 99%

“…Recall the transition matrix in Example 3.1. The Markov process that is defined by the transition matrix P β has stationary distribution 0, 1 3 , 1 3 , 1 3 , 0 . This means that after a very long time it will have spent the same amounts of time in π 1 , π 2 , and π 3 , while it will not have spent any time in π 0 or π 4 .…”

Section: Example 33mentioning

confidence: 99%

“…As the payoffs of all players are determined by a partition π , there is no need to explicitly consider the set of core payoff vectors 2. Recently,[1] have proposed a solution to the roommate problem that is based on the credibility of deviations. They show, in particular, that if one allows for "weak" deviations, then existence is guaranteed.…”

mentioning

confidence: 99%

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Farsighted Rationality in Hedonic Games

Demeze-Jouatsa

Karos

2022

Dyn Games Appl

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We consider a hedonic coalition formation game in which a coalition chooses for each partition of the player set the probability with which it forms and thereby destroys the current partition. These probabilities are commonly known so that farsighted players know at every partition what future partitions, and hence payoffs, will be reached with what probability. Thus, players can make rational decisions about the moves they support. We show that if coalitions make mistakes with small but positive probability, then there is a behavior profile in which no coalition has a profitable one-shot deviation.

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Section: Hedonic Gamesmentioning

confidence: 99%

Section: Example 33mentioning

confidence: 99%