arXiv subjects

Robert P. Gilles

Publications and source records attributed to Robert P. Gilles.

10 recordsLinked to original sources

arXiv2026

Second-Order Potentials for Finite Games: Existence, Characterisation, and Game Decomposition

Monderer and Shapley (1996) showed that a game is a potential game precisely when the players' second-order cross-differences agree pair by pair. This paper asks what can be built from them when the agreement fails. The resulting MS-potential, assembled from their common-interest part, is unique up to separable payoff terms and exists precisely when a higher-order MS-condition holds; on exact potential games it recovers the potential up to the players' main effects. A least-squares construction extends the MS-potential to all finite games and induces the \MS-decomposition: every game splits into a common-interest MS-potential game and a residual absorbing every player's individualistic effects. Everything read off the second differences is invariant under the transformations that leave strategic content untouched, relabelling, non-strategic translation and action duplication, where the CMOP decomposition is not; only the least-squares extension fails, since it averages and centres. The central result is an identity: when all players have equally many actions, an augmentation of the MS-potential coincides, up to the additive constant, with the potential of Candogan et al. (2011). If action counts are unequal they diverge, and no bound on that divergence is established here. Both rest on the same uniform weighting of the players' actions.

cs.GT↗

arXiv2026

Construction of Compromise Values for Cooperative Games

We explore a broad class of values for cooperative games in characteristic function form, known as compromise values. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs. We identify subclasses of games that admit non-trivial efficient allocations within the considered bounds, which we call \emph{bound-balanced games}. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using variants of the minimal rights property and restricted proportionality. We introduce two construction methods for properly devised compromise values. Under mild conditions, one can use either a lower or an upper bound to construct a well-defined compromise value. Based on these methods, we construct and axiomatise various well-known and new compromise values, including the $τ$-, the $χ$-, the Egalitarian, the Gately, the CIS-, the PANSC-, the EANSC-, and the new KM-values. We conclude that this approach establishes a common foundation for a wide range of different values.

econ.TH↗

arXiv2026

Structured Production Systems: Viability

This paper introduces a novel framework for analysing equilibrium in structured production systems that incorporate a static social division of labour, distinguishing between consumption goods traded in competitive markets and intermediate goods exchanged through bilateral relationships. We develop the concept of viability -- the requirement that all producers earn positive incomes, as a foundational equilibrium prerequisite. Our main theorem establishes that a structured production system is viable if and only if it is coherent, admitting no circular conversion processes that yield no net output, which in turn is equivalent to the non-singularity of its matrix representation. We further investigate completely viable systems, in which viable prices exist for all consumption good price vectors. We show that complete viability stands exactly between two input restrictions: it is guaranteed in coherent systems where no consumption good is used as an input in production, and it requires that no consumption good is used as an input in the production of another consumption good. The analysis thus reveals fundamental relationships between the architectural design of production systems and their economic sustainability. Our framework also contributes to the literature on the existence of positive output price systems and the Hawkins-Simon condition in input-output analysis.

econ.TH↗

arXiv2023

Game theoretic foundations of the Gately power measure for directed networks

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players--constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the $β$-measure, and construct an axiomatisation of the Gately measure.

cs.GT↗

arXiv2023

Gately Values of Cooperative Games

We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception introduced a bargaining solution that minimises the maximal quantified ``propensity to disrupt'' the negotiation process of the players over the allocation of the generated collective payoffs. Gately's solution concept is well-defined for a broad class of games. We also consider a generalisation based on a parameter-based quantification of the propensity to disrupt. Furthermore, we investigate the relationship of these generalised Gately values with the Core and the Nucleolus and show that Gately's solution is in the Core for all regular 3-player games. We identify exact conditions under which generally these Gately values are Core imputations for arbitrary regular cooperative games. Finally, we investigate the relationship of the Gately value with the Shapley value.

econ.TH↗

arXiv2021

Emergent Collaboration in Social Purpose Games

We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players. We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of \emph{strict} social purpose games. Due to the nature of the partial cooperative leadership equilibrium, stable coalitions of cooperators reflect a limited form of farsightedness in their formation. As a particular application, we study the tragedy of the commons game. We show that there emerges a single stable coalition of cooperators to curb the over-exploitation of the resource.

cs.GT↗

arXiv2020

Building social networks under consent: A survey

This survey explores the literature on game-theoretic models of network formation under the hypothesis of mutual consent in link formation. The introduction of consent in link formation imposes a coordination problem in the network formation process. This survey explores the conclusions from this theory and the various methodologies to avoid the main pitfalls. The main insight originates from Myerson's work on mutual consent in link formation and his main conclusion that the empty network (the network without any links) always emerges as a strong Nash equilibrium in any game-theoretic model of network formation under mutual consent and positive link formation costs. Jackson and Wolinsky introduced a cooperative framework to avoid this main pitfall. They devised the notion of a pairwise stable network to arrive at equilibrium networks that are mainly non-trivial. Unfortunately, this notion of pairwise stability requires coordinated action by pairs of decision makers in link formation. I survey the possible solutions in a purely non-cooperative framework of network formation under mutual consent by exploring potential refinements of the standard Nash equilibrium concept to explain the emergence of non-trivial networks. This includes the notions of unilateral and monadic stability. The first one is founded on advanced rational reasoning of individuals about how others would respond to one's efforts to modify the network. The latter incorporates trusting, boundedly rational behaviour into the network formation process. The survey is concluded with an initial exploration of external correlation devices as an alternative framework to address mutual consent in network formation.

econ.TH↗

arXiv2018

The Core of an Economy with an Endogenous Social Division of Labour

This paper considers the core of a competitive market economy with an endogenous social division of labour. The theory is founded on the notion of a "consumer-producer", who consumes as well as produces commodities. First, we show that the Core of such an economy with an endogenous social division of labour can be founded on deviations of coalitions of arbitrary size, extending the seminal insights of Vind and Schmeidler for pure exchange economies. Furthermore, we establish the equivalence between the Core and the set of competitive equilibria for continuum economies with an endogenous social division of labour. Our analysis also concludes that self-organisation in a social division of labour can be incorporated into the Edgeworthian barter process directly. This is formulated as a Core equivalence result stated for a Structured Core concept based on renegotiations among fully specialised economic agents, i.e., coalitions that use only fully developed internal divisions of labour. Our approach bridges the gap between standard economies with social production and coalition production economies. Therefore, a more straightforward and natural interpretation of coalitional improvement and the Core can be developed than for coalition production economies.

econ.TH↗

arXiv2014

Critical Nodes In Directed Networks

Critical nodes or "middlemen" have an essential place in both social and economic networks when considering the flow of information and trade. This paper extends the concept of critical nodes to directed networks. We identify strong and weak middlemen. Node contestability is introduced as a form of competition in networks; a duality between uncontested intermediaries and middlemen is established. The brokerage power of middlemen is formally expressed and a general algorithm is constructed to measure the brokerage power of each node from the networks adjacency matrix. Augmentations of the brokerage power measure are discussed to encapsulate relevant centrality measures. We use these concepts to identify and measure middlemen in two empirical socio-economic networks, the elite marriage network of Renaissance Florence and Krackhardt's advice network.

cs.SI↗

arXiv2013

Platform Competition as Network Contestability

Recent research in industrial organisation has investigated the essential place that middlemen have in the networks that make up our global economy. In this paper we attempt to understand how such middlemen compete with each other through a game theoretic analysis using novel techniques from decision-making under ambiguity. We model a purposely abstract and reduced model of one middleman who pro- vides a two-sided platform, mediating surplus-creating interactions between two users. The middleman evaluates uncertain outcomes under positional ambiguity, taking into account the possibility of the emergence of an alternative middleman offering intermediary services to the two users. Surprisingly, we find many situations in which the middleman will purposely extract maximal gains from her position. Only if there is relatively low probability of devastating loss of business under competition, the middleman will adopt a more competitive attitude and extract less from her position.

cs.GT↗