Stochastic bankruptcy games

Habis, Helga; Herings, P. Jean-Jacques

doi:10.1007/s00182-012-0350-x

Cited by 25 publications

(13 citation statements)

References 14 publications

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“…He followed Shapley's characterization for this allocation procedure to the links. The weighted Shapley value defined by Kalai and Samet (1987) was generalized to communication situations in Haeringer (1999) and to hierarchical structures in Slikker and van den Nouweland (2000a). van den Nouweland and Slikker (2012) characterized the position value for network situations where no condition on the underlying network is required.…”

Section: Related Literaturementioning

confidence: 99%

“…They show the non-emptiness of the weak sequential core under some condition. Habis and Herings (2013) study stochastic bankruptcy games and use the weak sequential core as a solution concept for such games. Lehrer and Scarsini (2013) consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations.…”

Section: Related Literaturementioning

confidence: 99%

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An allocation rule for dynamic random network formation processes

2015

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Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Time series of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and ruled by a stochastic process, typically a Markov chain. We propose the link-based scenario allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process, we recover the link-based flexible network allocation rule of Jackson (Games Econ Behav 51:128-154, 2005a).

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Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

An allocation rule for dynamic random network formation processes

2015

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“…version of the rationing problem: Ertemel and Kumar ( [5]) characterize versions of our Ex-post and Ex-Ante Service rules in a state contingent claims framework; while Habis and Herings ( [7]) and Xue ([21]) consider stochastic versions of the uniform gains rule.…”

Section: Relation To the Literaturementioning

confidence: 99%

“…Clearly a cost additive rule takes the form e y(Q; p; c) = X a2A y(a; Q; p)c a (7) where (N ) is the N -simplex and y(a; Q; p) 2 (N ) speci…es how the liability shares for project a.…”

Section: Three Separability Properties 41 Cost Additivitymentioning

confidence: 99%

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Sharing the cost of risky projects

Hougaard

Moulin

2017

Econ Theory

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Users share the cost of unreliable non rival projects (items). For instance, industry partners pay today for R&D that may or may not deliver a cure to some viruses, agents pay for the edges of a network that will cover their connectivity needs, but the edges may fail, etc.. Each user has a binary inelastic need that is served if and only if certain subsets of items are actually functioning. We ask how should the cost be divided when individual needs are heterogenous. We impose three powerful separability properties:Independence of Timing ensures that the cost shares computed ex ante are the expectation, over the random realization of the projects, of shares computed ex post. Cost Additivity together with Separability Across Projects ensure that the cost shares of an item depend only upon the service provided by that item for a given realization of all other items.Combining these with fair bounds on the liability of agents with more or less ‡exible needs, and of agents for whom an item is either indispensable or useless, we characterize two rules: the Ex Post Service rule is the expectation of the equal division of costs between the agents who end up served; the Needs Priority rule splits the cost …rst between those agents for whom an item is critical ex post, or if there are no such agents between those who end up being served.

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Proportional rules for state contingent claims

Ertemel

Kumar

2017

Int J Game Theory

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We consider rationing problems where the claims are state contingent.Before the state is realized individuals submit claims for every possible state of the world. A rule distributes resources before the realization of the state of the world. We introduce two natural extensions of the proportional rule in this framework, namely, the ex-ante proportional rule and the ex-post proportional rule, and then we characterize them using standard axioms from the literature.

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Stochastic bankruptcy games

Cited by 25 publications

References 14 publications

An allocation rule for dynamic random network formation processes

An allocation rule for dynamic random network formation processes

Sharing the cost of risky projects

Proportional rules for state contingent claims

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