The importance of reputation in the auditing of companies: A game theory analysis

Numerous, mainly empirical, studies of auditing behaviour have recently looked at the “reputation” of the auditor and the size of fees it attracts. Our model of the auditing market advances the study of the fundamental principles involved in determining behaviour in relation to the rewards and penalties using an extensive-form game of the auditing process. We set up a two-player fraud detection game with bribes, bonuses and fines faced by an auditor. Our model yields that the auditor’s reputation, reflected in the size of bonuses, is critical to establishing a non-fraudulent behaviour by the client. Hence the model confirms expected behaviour. We further find the new insight, that while the existence of penalties deters fraud by the client, their size is not critical. This is a new understanding of what determines auditor behaviour. It is the perception of a possible penalty that moves the auditor in the direction of executing a thorough investigation using his acquired expertise

A Temporal Framework for Hypergame Analysis of Cyber Physical Systems in Contested Environments

Game theory is used to model conflicts between one or more players over resources. It offers players a way to reason, allowing rationale for selecting strategies that avoid the worst outcome. Game theory lacks the ability to incorporate advantages one player may have over another player. A meta-game, known as a hypergame, occurs when one player does not know or fully understand all the strategies of a game. Hypergame theory builds upon the utility of game theory by allowing a player to outmaneuver an opponent, thus obtaining a more preferred outcome with higher utility. Recent work in hypergame theory has focused on normal form static games that lack the ability to encode several realistic strategies. One example of this is when a player’s available actions in the future is dependent on his selection in the past. This work presents a temporal framework for hypergame models. This framework is the first application of temporal logic to hypergames and provides a more flexible modeling for domain experts. With this new framework for hypergames, the concepts of trust, distrust, mistrust, and deception are formalized. While past literature references deception in hypergame research, this work is the first to formalize the definition for hypergames. As a demonstration of the new temporal framework for hypergames, it is applied to classical game theoretical examples, as well as a complex supervisory control and data acquisition (SCADA) network temporal hypergame. The SCADA network is an example includes actions that have a temporal dependency, where a choice in the first round affects what decisions can be made in the later round of the game. The demonstration results show that the framework is a realistic and flexible modeling method for a variety of applications

Rubinstein's bargaining model

Treballs Finals del Doble Grau d'Administració i Direcció d'Empreses i de Matemàtiques, Facultat d'Economia i Empresa i Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Curs: 2020-2021 , Tutors: Xavier Jarque i Javier Martínez de Albéniz[eng] Rubinstein's bargaining model de nes a multi-stage non-cooperative game in extensive form with complete information. It is applied to two-person games that feature alternating o ers through an in nite time horizon. We study the process of bargaining due to Rubinstein (1982) | from his seminal paper Perfect equilibrium in a bargaining model. Firstly, we present in detail this model. The fundamental assumption is that the players are impatient and the main result provides conditions under which the game has a unique subgame perfect equilibrium. The result gives a characterization of this equilibrium and features the fact that bargaining implies costs for the agents (time and money). In addition, we introduce a variation of the model which was revisited some years later (1988). To do it, it uses new utility functions which are used to arrive to the same conclusion of the original model. Finally, we present an extension of the model of bargaining to the war of attrition (Ponsati and S akovics, 1995), using games with incomplete information. They introduce the deadline e ect.[cat] El model de negociació de Rubinstein defineix un joc no cooperatiu format per diverses etapes en forma extensiva amb informació completa. S'aplica a jocs de dos agents en els quals es presenten ofertes alternades al llarg d'un període de temps eventualment infinit. Estudiem el procés de negociació ideat per Rubisntein (1982) | del seu article decisiu Perfect equilibrium in a bargaining model. En primer lloc, presentam detalladament aquest model. La suposició fonamental és que els jugadors són impacients i el resultat final proporciona condicions sota les quals el joc té un únic equilibri perfecte en subjocs. El resultat dona una caracterització d'aquest equilibri i mostra el fet que la negociació suposa uns costos per als agents (temps i diners). A més a més, introduïm una variació del model que va ser revisada alguns anys després (1988). Per fer-ho, s'utilitzen noves funcions d'utilitat per arribar a la mateixa conclusió del model original. Finalment, presentam una extensió del model de negociació a la guerra de desgast (Ponsati i Sákovics, 1995), mitjan cant jocs amb informació incompleta. Introdueixen l'efecte de la data límit

One Step at a Time: Does Gradualism Build Coordination?

We study how gradualism -- increasing required levels (“thresholds”) of contributions slowly over time rather than requiring a high level of contribution immediately -- affects individuals’ decisions to contribute to a public project. Using a laboratory binary choice minimum-effort coordination game, we randomly assign participants to three treatments: starting and continuing at a high threshold, starting at a low threshold but jumping to a high threshold after a few periods, and starting at a low threshold and gradually increasing the threshold over time (the “gradualism” treatment). We find that individuals coordinate most successfully at the high threshold in the gradualism treatment relative to the other two groups. We propose a theory based on belief updating to explain why gradualism works. We also discuss alternative explanations such as reinforcement learning, conditional cooperation, inertia, preference for consistency, and limited attention. Our findings point to a simple, voluntary mechanism to promote successful coordination when the capacity to impose sanctions is limited.Gradualism; Coordination; Cooperation; Public Goods; Belief-based Learning; Laboratory Experiment

Spatial competition of learning agents in agricultural procurement markets

Spatially dispersed farmers supply raw milk as the primary input to a small number of large dairy-processing firms. The spatial competition of processing firms has short- to long-term repercussions on farm and processor structure, as it determines the regional demand for raw milk and the resulting raw milk price. A number of recent analytical and empirical contributions in the literature analyse the spatial price competition of processing firms in milk markets. Agent-based models (ABMs) serve by now as computational laboratories in many social science and interdisciplinary fields and are recently also introduced as bottom-up approaches to help understand market outcomes emerging from autonomously deciding and interacting agents. Despite ABMs' strengths, the inclusion of interactive learning by intelligent agents is not sufficiently matured. Although the literature of multi-agent systems (MASs) and multi-agent economic simulation are related fields of research they have progressed along separate paths. This thesis takes us through some basic steps involved in developing a theoretical basis for designing multi-agent learning in spatial economic ABMs. Each of the three main chapters of the thesis investigates a core issue for designing interactive learning systems with the overarching aim of better understanding the emergence of pricing behaviour in real, spatial agricultural markets. An important problem in the competitive spatial economics literature is the lack of a rigorous theoretical explanation for observed collusive behavior in oligopsonistic markets. The first main chapter theoretically derives how the incorporation of foresight in agents' pricing policy in spatial markets might move the system towards cooperative Nash equilibria. It is shown that a basic level of foresight invites competing firms to cease limitless price wars. Introducing the concept of an outside option into the agents' decisions within a dynamic pricing game reveals viihow decreasing returns for increasing strategic thinking correlates with the relevance of transportation costs. In the second main chapter, we introduce a new learning algorithm for rational agents using H-PHC (hierarchical policy hill climbing) in spatial markets. While MASs algorithms are typically just applicable to small problems, we show experimentally how a community of multiple rational agents is able to overcome the coordination problem in a variety of spatial (and non-spatial) market games of rich decision spaces with modest computational effort. The theoretical explanation of emerging price equilibria in spatial markets is much disputed in the literature. The majority of papers attribute the pricing behavior of processing firms (mill price and freight absorption) merely to the spatial structure of markets. Based on a computational approach with interactive learning agents in two-dimensional space, the third main chapter suggests that associating the extent of freight absorption just with the factor space can be ambiguous. In addition, the pricing behavior of agricultural processors – namely the ability to coordinate and achieve mutually beneficial outcomes - also depends on their ability to learn from each other