Last
update 2011/01/18
Research in Game theory
Working Papers
§ The
value in games with restricted cooperation (2009)
§ Abstract: Given a cooperative game, a
restriction in cooperation is given by a set system, which specifies the set of
feasible coalitions that can be formed. In this setting, the Shapley value is
defined following the random order approach: the value is the expected marginal
contribution of the player to its predecessors in every order. The main
difference from previous approaches, which are based on the restriction over
the feasible set of orderings, is that all orderings are considered as
feasible, and that the set system will determine only which coalitions are
formed when players arrive successively in every order.
§ The
coalitional value in finite-type continuum games (2009)
§ Abstract: The coalitional value [Owen,
Values of games with a priori unions. In: Hein R, Moeschlin
O (Eds), Essays in Mathematical Economics and Game
Theory. Springer Verlag, 1977] is defined for the
class of continuos games with a finite type of
players. A formula for its computation is provided jointly with an axiomatic
characterization of it. The properties used are a natural extension in this
setting of the properties used in the characterization of the Owen's
coalitional value for games with a finite set of players.
§ A value
for cooperative games with a coalition structure (2011) (with Esther
Gutiérrez)
§ Abstract: A value for games with a
coalition structure is introduced, where the rules guiding the cooperation
among the members of the same coalition are different from the interaction
rules among coalitions. In particular, players inside a coalition exhibit a
greater degree of solidarity than they are willing to use with players outside
their coalition. The Shapley value [Shapley, 1953] is therefore used to compute
the aggregate payoffs of the coalitions, and the Solidarity value [Nowak and Radzik, 1994] to obtain the payoffs of the players inside
each coalition.
§ Strategic Interaction and Altruism (2011) (with Esther
Gutiérrez)
§ Abstract: We present a model
of non-cooperative bargaining among players in the setting of cooperative games
with transferable utility. In this model, the proposers are chosen randomly
and, after a proposal's rejection, every player has their own (and independent)
probability of leaving the game. The equilibrium proposals are characterized
and computed when the probabilities of leaving the game are smaller. These
limit proposals are called the weighted solidarity value. This value implies an
altruistic behavior between players as the null and dummy player properties are
not satisfied. When all probabilities are equal, this value coincides with the
Solidarity value [Nowak and Radzik, 1994]. Therefore
we can explain altruism as a natural behavior followed by selfish players in a
cooperative setting.
Published Papers
Ö Cooperative solutions on coalitional games
Ö
Power indices, graphs and social
choice
Pure
bargaining problems
§
§
§ Bargaining with ordinal and cardinal players (with Hans
Peters)
§Abstract: We consider bargaining problems with at least one
cardinal player and with ordinal
players, and provide a complete description of utility invariant solutions of
such problems for two players. For the n-person case we provide a procedure
that: (i) returns a given cardinal solution if there
are only cardinal players; (ii) is based on the ordinal solution for gradual bargaining problems, introduced by O'Neill et al. (2001),
for the ordinal players. Finally, we introduce the so-called cardinal
concession solution as another example of a utility invariant solution.
§Games & Economic Behavior Vol. 52 (1). p 20-33. July 2005.
§ Dynamics and Axiomatics of
the Equal Area Bargaining Solution (with Hans Peters)
§Abstract: We present an alternative
formulation of the two-person equal area bargaining solution based on a
dynamical process describing the disagreement point set. This alternative
formulation provides an interpretation of the idea of equal concessions.
Furthermore, it leads to an axiomatic characterization of the solution.
§International Journal of Game Theory Vol. 29 (1). p 81-92. February 2000.
§ Extension of the Perles-Maschler
Solution to N-Person Bargaining Games (with Esther Gutiérrez)
§Abstract: The superadditive solution for 2-person Nash
bargaining games was axiomatically defined in Perles/Maschler (1981). In Perles (1982)
it was shown that the axioms are incompatible even for 3-person bargaining
games. In this paper we offer a generalization method of this solution concept
for n-person games. In this method, the Kalai-Smorodinsky
solution (1975) is revealed as the rule followed to determine the movements
along the path of intermediate agreements.
§International Journal of Game Theory Vol. 23 (4). p 325-346, 1994.
Cooperative solutions on coalitional
games
§ Solidarity
in games with a coalition structure (with Esther Gutiérrez)
§Abstract: A new axiomatic
characterization of the two-step Shapley value (Kamijo
(2007)) is presented based in a solidarity principle for the members of a
union: when the game changes due to the addition or deletion of players outside
the union, all members of the union will share the same gains/losses
§Mathematical Social Sciences Vol. 60 (2010), p. 196-203. PDF_document
§
§ Random
Marginal and Random Removal Values
§We propose two
variations of the non-cooperative bargaining model for games in coalitional
form, introduced by Hart and Mas-Colell (1996a).
These strategic games implement, in the limit, two new NTU-values: The random
marginal and the random removal values. The main characteristic of these
proposals is that they always select a unique payoff allocation in NTU-games.
The random marginal value coincides with the Consistent NTU-value (Maschler and Owen, 1989) for hyperplane
games, and with the Shapley value for TU games (Shapley, 1953). The random removal
coincides with the solidarity value (Novak and Radzik,
1994) in TU-games. In large games we show that, in the special class of market
games, the random marginal value coincides with the Shapley NTU-value (Shapley,1969), and that the random removal value coincides with the
equal split value.
§ International Journal of Game Theory Vol. 37 (4). p. 533-564. 2008 PDF Document Erratum PDFDocument
§ The Serial
Principle and Restricted Balanced Contributions in Discrete Cost Sharing
Problems (with Juan Carlos Santos)
§Abstract: We show that the axioms of Efficiency, Serial
Principle and Restricted Balanced Contributions, characterize the Moulin's rule
(Moulin, 1995) in discrete cost allocation problems.
§ TOP Vol.
14 (2). p. 343-353. April 2006. PDF Document
§ A Value for Mixed Action-Set Games (with Juan Carlos
Santos)
§Abstract: We extend the Aumann-Shapley value to mixed action-set games, i.e.,
multilevel TU games where there are simultaneously two types of players:
discrete players that possess a finite number of activity levels in which they
can join a coalition, and continuous players that possess a continuum of
levels.
§International Journal of Game Theory Vol. 30 (1). p 61-78. 2001.
§ Prices in Mixed Cost Allocation Problems (with Juan Carlos Santos)
§Abstract: We consider mixed cost allocation problems, i.e.,
joint cost problems that involve two types of heterogeneous outputs, divisible
and indivisible. The Aumann-Shapley price mechanism
is extended to this setting. We also present a set of properties which
characterize this cost sharing rule.
§Games & Economic Behavior Vol. 37 (2). p 243-58. November 2001.
§ Replication Invariance on NTU Games ( with Inaki Garcia, Jose M Zarzuelo)
§Abstract: Two concepts of replication (conflictual and non-conflictual)
are extended from the class of pure bargaining games to the class of NTU games.
The behavior of the Harsanyi,
Shapley NTU, Egalitarian and Maschler-Owen solutions
of the replica games is compared with that of the Nash and Egalitarian
solutions in pure bargaining games.
§International Journal of Game Theory Vol. 29 (4). p 473-86. 2000.
§ Weighted Weak Semivalues (with Juan Carlos Santos)
§Abstract: We introduce two new value solutions: weak semivalues and weighted weak semivalues.
They are subfamilies of probabilistic values, and they appear by adding the
axioms of balanced contributions and weighted balanced contributions
respectively. We show that the effect of the introduction of these axioms is
the appearance of consistency in the beliefs of players about the game.
§International Journal of Game Theory Vol. 29 (1). p 1-9. February 2000.
§ The Multichoice Consistent
Value (with Esther Gutierrez, Juan Carlos Santos)
§Abstract: We consider multichoice
NTU games, i.e., cooperative NTU games in which players can participate in the
game with several levels of activity. For these games, we define and
characterize axiomatically the multichoice consistent
value, which is a generalization of the consistent NTU value for NTU games and
of the multichoice value for multichoice
TU games. Moreover, we show that this value coincides with the consistent NTU
value of a replicated NTU game and we provide a probabilistic interpretation.
§International Journal of Game Theory Vol. 29 (2). p 177-88. July 2000.
§ A Value for Multichoice
Games (with Juan Carlos Santos)
§Abstract: A multichoice
game is a generalization of a cooperative TU game in which each player has
several activity levels. We study the solution for these games proposed by Van
Den Nouweland et al. (1995). We show that this
solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995). Also, we
show that the Aumann-Shapley value for continuum
games can be obtained as the limit of multichoice
values for admissible convergence sequences of multichoice
games. Finally, we characterize this solution by using the axioms of balanced
contributions and efficiency.
§Mathematical Social Sciences Vol. 40 (3). p 341-54. November 2000.
§ Potentials in Cooperative TU-Games (with Juan Carlos Santos)
§Abstract: This paper is
devoted to the study of solutions for cooperative TU-games which admit a
potential function, such as the potential associated with the Shapley value
(introduced by Hart and Mas-Colell). We consider the
finite case and the finite type continuum. Several
characterizations of this family are offered and, as a main result, it is shown
that each of these solutions can be obtained by applying the Shapley value to
an appropriately modified game. We also study the relationship of the potential
with the noncooperative potential games, introduced
by Monderer and Shapley, for the multilinear
case in the continuum finite type setting.
§Mathematical Social Sciences Vol. 34 (2). p 175-90. October 1997.
§ A Prekernel Characterization
by Means of Stability Properties (with
Esther Gutierrez)
§Abstract: We define two new
properties for payoff allocations in the set of pre-imputations of a
TU-cooperative game: Strong stability and balanced
surplus property. By means of these properties we give a new
characterization of the Prekernel of a game.
Also a characterization of the Least-core of a game is done in terms of
strong stability.
§TOP Vol 4 (2). p 257-267. December 1996.
§ The Principle of Balanced Contributions and
Hierarchies of Cooperation (vith
J Javier Lasaga, Eyal Winter)
§Abstract: The principle of
balanced contributions has appeared repeatedly in the literature on the Shapley
value. This principle is akin to the reciprocity properties shared by almost
all cooperative solution concepts. We provide a new axiomatization
for the level structure value. This axiomatization
has the advantage that it can be applied to many important subdomains of TU
games. We use the Hart-Mas-Colell potential function
as a tool to prove our main result, and establish another interesting
characterization for the value as a by-product.
§Mathematical Social Sciences Vol. 31 (3). p 171-82. June 1996.
§ On the Axiomatization of the
Tau-Value (vith S.H. Tijs, F. Valenciano,
J.M. Zarzuelo)
§Abstract: The Tau-value is a
solution concept for a subclass of games with transferable utility introduced
and axiomatized by Tijs. In
this note an alternative characterization of the Tau-value
by means of five axioms is offered. Two of them are well-known: efficiency and
translation equivalence; the other three relate the solution of a game with the
minimal and maximal aspiration vectors involved in the definition of the value.
§TOP Vol 3(1). p 35-46. June 1995.
Power indices, graphs and social choice
§
§ Scoring Rules: A Cooperative Game-Theoretic Approach (with Esther Gutierrez, Inaki Garcia)
§Abstract: In this work we define the game of the alternatives for each preference profile, and establish
relations between scoring rules and cooperative solution concepts for that
game, such as the family of semivalues and the family
of least square values.
§Social Choice & Welfare Vol. 16 (3). p 491-512. May 1999.
§ Values of games with probabilistic graphs (vith J
Javier Lasaga , Anne van den Nouweland )
§Abstract: In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model
of games with communication restrictions by Myerson (1977). In the Myerson
model each pair of players is joined by a link in the graph if and only if
these two players can communicate directly. The current paper considers a more
general setting in which each pair of players has some probability of direct
communication. The value is defined and characterized in this context. It is a
natural extension of the Myerson value and it turns out to be the Shapley value
of a modified game.
§Mathematical
Social Sciences Vol. 37 (1): p 79-95, Jan
1999.
§ Probabilistic Graphs and Power Indices: An Application
to the Spanish Parliament (with J Javier Lasaga)
§Abstract: In this paper we consider games with
probabilistic graphs. The model we develop is an extension of the model of games
with communication restrictions by Myerson (1977). In the Myerson model each
pair of players is joined by a link in the graph if and only if these two
players can communicate directly. The current paper considers a more general
setting in which each pair of players has some probability of direct
communication. The value is defined and characterized in this context. It is a
natural extension of the Myerson value and it turns out to be the Shapley value
of a modified game.
§Journal of Theoretical Politics Vol. 9 (4): p 477-502, October 1997.