My focus in the thesis is the efficiency/inefficiency presented by the selfish behavior of players in games and markets, and how to deal with the inefficiency. In the thesis, I consider both economic and computational efficiency in designing mechanisms for dividing a collection of individuals into teams (coalitions).
Towards Efficiency in Security Games
Multi-Defender Security Games
In this setting, I theoretically characterize Nash and approximate Nash equilibria as well as their efficiency. In the thesis, I characterize Nash and approximate equilibria among defenders and theoretically analyze the efficiency degradation due to the selfish behavior of defenders in multi-defender security games.
Multi-Defender Against Spear-Phishing Attacks
The externalities that users impose on each other thus become strategically significant, and no work to date analyzes the resulting strategic dynamics in the spearfishing context, although previous work has considered other, quite different, interdependent security problems. In the thesis, I study players' strategic behavior when there are multiple selfish defenders against spearfishing attacks, I analyze the existence and the efficiency of equilibrium, and propose a polynomial algorithm to find such an equilibrium if it exists.
Decentralization and Security in Traffic Light Control
29] proposed to represent the traffic lights by locally coupled phase oscillators, whose frequencies adapt to the minimum cycle of all nodes in the network. In the thesis, I use game-theoretic analysis on the traffic control system and design a scalable algorithm to approximate a Nash equilibrium in the system.
Toward Efficiency in Coalition Formation
Coalition Formation Mechanisms
Two special cases of the coalition formation mechanism design problem have received considerable attention: two-sided matching markets [37], such as matching medical school residents with residency programs, and one-sided matching or assignment problems [40, 41], such as e.g. school choice and course allocation (the latter abstracted as combinatorial assignment). In the general coalition formation problems, random serial dictatorship (RSD) is to our knowledge the only mechanism that is incentive compatible and ex post Pareto efficient [ 43 , 44 ].
Mechanism Design for the Roommates Problem
Towards Efficiency by Introducing a Secondary Market
In the second stage (ie, the secondary market), demand uncertainty is resolved, all required resources are used, and the remaining resources can be freely traded. The secondary market, on the other hand, creates an implicit dependence between the optimal decisions in the first stage.
Stackelberg Security Games
And the Stackelberg model has been adopted in many real-world situations, such as fishery protection [61], patrolling to protect ferries [62], forest land [63] and wildlife protection [64], etc. those applications, the Stackelberg model has also been used to study some problems that do not look at all like typical security games, such as adversarial machine learning [65], privacy-preserving data sharing [66], vaccine design [67 ], etc.
Security Games with Multiple Defenders
A natural extension of interdependent security games, the interdependent defense games [71], considers an attacker acting simultaneously with the defenders, rather than after observing the joint defense configuration. In security games with multiple defenders, players' decisions are often correlated, and the interdependence between players can often be modeled as a network structure.
Security Games for Defending Against Cyber Attacks
However, an overly sensitive intrusion detection system, which produces a large number of false alarms, imposes extremely high operational costs. 85] propose a game-theoretic model in the Man-in-the-Middle (MITM) attack and model the strategic interaction between the Man-in-the-Middle (MITM) attacker and multiple defenders as a game of simultaneous moves.
Hedonic Coalition Formation
There are also some subsequent works that investigate agent cooperation in coalition formation (such as A potentially infinitely long coalition formation process in the context of hedonic games was studied in [94].
Matching and Roommates Problem
Gale and Shapley [46] also note that consistent results do not necessarily exist in the roommate problem. Some other works in the roommate problem try to propose another solution concept, which is guaranteed to exist, in the roommate problem, such as Q-stable matching [112].
Secondary Markets
130] provide an overview of applications of cooperative game theory in the management of centralized inventory systems. Lee and Whang [131] discuss the impact of the secondary market on the supply chain problem, which is very relevant to mine.
Toward Efficiency: Security Game 23
Problem Setting
In this thesis I use a natural rule where the attacker uniformly and randomly chooses a target from the set of all best responses. We call the corresponding solution concept (which is a refinement of the perfect subgame equilibrium of our game) the Stackelberg mean-case equilibrium (ASE). Average Stackelberg equilibrium) A strategy profile (q,p) is ASE if each defender's strategy is the best response, taking the strategies of other defenders as given and assuming that the attacker will always choose a best response strategy play, where ties are evenly broken randomly if there are multiple best-response strategies.
Equilibrium Analysis
- Equilibrium Analysis on a Baseline Model
- Equilibrium Analysis of the General Model
We claim that the equilibrium (Ω−Uu)(kc−Ucnk c+Uu) can occur only if all targets have the same coverage probability q. First, we claim that we can obtain optimal social welfare only if all targets have the same coverage probability q.
Conclusion
I provide a characterization of the equilibria and present a polynomial-time algorithm for computing the multi-defender Stackelberg equilibrium. Surprisingly, I demonstrate that multi-defender Stackelberg equilibria need not exist, and it is socially optimal if it does exist, which is very different from the result I obtain from general multi-defender security games.
Problem Settings
As is typical in the literature, we study them using two different solution concepts, the multi-defender Stackelberg equilibrium and the Nash equilibrium. We solve this model using the concept of Stackelberg multiple defender equilibrium (SMDE), which is defined as follows.
![Figure IV.1: False-negative to false-positive tradeoff curves for the two datasets used in [1]](https://thumb-ap.123doks.com/thumbv2/123dok/10740174.0/53.918.175.803.104.385/figure-false-negative-false-positive-tradeoff-curves-datasets.webp)
Equilibrium Analysis
- Preliminaries
- Stackelberg Multi-Defender Equilibrium
A strategy profile is an SMDE if each user's strategy is a best response, taking the user's strategies as given and assuming that the attacker will always play a best response strategy. First, I show that in an SMDE the attacker plays a pure strategy and the users play fu1or fu0.
Conclusion
So far, we have characterized SMDEs that arise due to the selfish decisions of users. In this chapter, I propose a systematic approach to the decentralized control problems described in the introduction by considering a multi-intersection scenario in which a) traffic light controllers consider relative queue lengths to determine the red-green state of traffic lights per intersection, b) all-light controllers must be designed to work together to optimize the overall performance of the traffic network, c) sensors feeding data to controllers are vulnerable to denial of service attacks, and d) intersections are partitioned. between a set of actors who have their own objectives regarding congestion within their local municipal region, which are generally not aligned with the global interests of the entire transport network.
Traffic Network Model
In the chapter, I will generalize the control logic to the cases with multiple intersections and correspondingly with multiple traffic lights. For each vehicle vi traveling in the traffic system, latency li measures the time taken for the vehicle from entering the system to exiting the system.
Optimizing Traffic Network Configuration
Resilient Traffic Network Control
A Stackelberg equilibrium of the resilient network control game Γ is (s∗,r∗(s∗)), such that∑i,krik=1, r∗ letcyL(s∗,r(s)) maximize, etc∗ minimize the resulting maximum latencyL(s,r∗(s)). The goal of resilient network control is to choose s∗ that is part of a Stackelberg equilibrium that accounts for the attacker's best response.
Decentralized Control
Single-defender, no striker Single-defender one-striker, no resilient single-defender one-striker, resilient. I propose a resilient extension of BRA, shown in Algorithm 6, in which each best response iteration now accounts for the attacker's sensor DoS attack strategy.
Evaluation and Results
The test results can be seen in figures V.3, V.4, V.5 and V.6, which show the total weighted average delay L as a function of fire engine weights. When there is a single defender (Figure V.3) and no attacker, we obtain a relatively low L (using Algorithm 2).
Conclusion
Toward Efficiency: Coalition Formation Mechanism 65
Problem Setting
Team Formation Games and Rotating Proposer Mechanism
If everyone accepts j∈T\i, the coalitionT is added to the partitionπ, all players are removed from the game and outO, and the game continues to the next round, unless there are no players left (in which case the game ends with a partitionπ) . For each profile, if all players truthfully report their preferences, the equilibrium outcomes of the game have some good properties that are therefore inherited by RPM.
Implementing RPM
- Preprocessing and Pruning
- Approximate RPM for the Roommate Problem
- Heuristic Rotating Proposer Mechanism (HRPM)
Given the corresponding RPM subgame, let Uj(i) denote the set of possible teammates that j prefers, and let Uj(j) be the set of feasible teammates that j prefers to be alone. Then, for each such teammate k, we find in the percentage of possible teammates who are no longer preferred by receiver j.
Experiment
- Data Sets
- Computing and Approximating RPM
- Utilitarian Social Welfare
- Fairness
- Incentive Compatibility
Figures VI.3a and VI.3b depict the mean utilitarian social welfare for RSD and RPM in the roommate problem on scale-free networks, Karate club networks, and Newfrat data. In the trio-roommate problem, HRPM (β =0.6) is much fairer than RSD and OPOP, except for the correlation on the Newfrat data, in which OPOP is better, as shown in Figures VI.7 and VI.8.
Conclusion
In the thesis, I consider a new perspective on the roommate problem based on automatic mechanism design (AMD) [50]. However, the application of AMD to matching problems in general, and the roommate problem in particular, faces a number of challenges.
The Roommates Model
- Incentive Compatibility
- Individual Rationality
- Social Welfare
We define rui(π(i)) as the cardinal utility of the measure assigned to playeri in the matchingπ. In the roommate problem, this can be represented by constraints ∀ ,i,M(,i)i{i}, which for cardinal preferences become sui(M(,i))≥ui({i}).
Restricted Incentive Compatibility
- Promotion-One Incentive Compatibility
- Promotion and Permutation Incentive Compatibility
We knew that DA is incentive compatible for the proposing side (i.e. women), so we will show that it is also promotion-one incentive compatible for the men. Showing that this is IC for the limited subset of promotion-one manipulations, together with this anecdotal claim, provides evidence that promotion-one manipulations may be the most salient manipulations in matched settings.
Automated Mechanism Design for Roommates Problem
- AMD That Maximizes Social Welfare
- AMD with Approximate Permutation Incentive Compatibility
- Heuristic Approaches with Promotion-One Manipulations
The constraint (VII.3b) can make sure that player cannot win more thanε∗ by matching with any player inRi. Here, PMSW(·) denotes the assignment that maximizes social welfare (i.e., solves program (VII.2)), and sw(·) denotes the social welfare of an assignment.
Experiments
HereUi is the utility obtained from the ranking of one player (jin in this case) in the first position, and -{i,j}is the profile of all players except j. Our main observation here, however, is that our three algorithmic approaches (Algorithms 1–3) yield similar social welfare when α ≤0.3 (within 0.01).
Conclusion
However, the difference is not so significant for BA networks, although we can also see the superiority of Algorithm 2 and Algorithm 3.
Toward Efficiency: Secondary Market 100
Model
- Background: The Newsvendor Model
- The Newsvendor Model with a Secondary Market
In the first stage (primary market), all players' demands are unknown (but their distributions are assumed to be known) and each player i∈N orders xi units of the resource at the unit price. For each player, the quantity of the resource bought or sold in the secondary market is jointly determined by x, Q, and P(Q,x).
Large Markets: Asymptotic Analysis
- Market Clearing Price in Secondary Market
- Players’ Influence on the Price
- Existence and Characteristics of the asymptotic Nash Equilibrium . 113
Proposition VIII.2.1 and VIII.2.2 together we conclude that the influence of an individual on the price on the secondary market is Omax(x . max,qmax) min(σ√). Because the price on the primary market is equal to the expected price in a secondary market, c.
Small Markets: Two Players
- Nash Bargaining Price
- Existence of Pure Strategy Nash Equilibrium between Two Players 124
Specifically, we consider the Nash bargaining solution concept[146] to identify the price in the secondary market. Assuming that the symmetric equilibrium in the two-player game is (xe,xe), we are ready to compare ∗,xe, andx# for the aggregate order and compare SW2nd(x∗),SW2nd(xe) and SW#(x# ) )for social welfare.
Conclusion
InProceedings of the 11th International Conference on Outonome Agents and Multiagent Systems - Volume 1, AAMAS ’12, pages 13–20, Richland, SC, 2012. InProceedings of the 7th International Joint Conference on Outonome Agents and Multiagent Systems - Volume 2, AAMAS.
Price of Anarchy when v ≥ c
- False-negative to false-positive tradeoff curves for the two datasets used
- Intersection
- Emergency Vehicle Scenario
- Comparison with single-defender
- Comparison with no attacker (baseline) configuration
- Comparison with resilient single-defender configuration
- Comparison with decentralized solutions
- Time consumed ratio (with IMS/without IMS) for RPM on scale-free
- Time consumed and average proportion of same coalitions
- Utilitarian social welfare for roommate problem
- Utilitarian social welfare for trio-roommate problem
- Maximum team utility difference for the roommate problem
- Pearson Correlation for the roommate problem
- Maximum Coalition Utility Difference for the trio-roommate problem
- Pearson Correlation for the trio-roommate problem
- Social welfare on ER (left) and BA (right) networks
- Maximum benefit from deviation on ER (left) and BA (right) networks
- Proportion of players who can benefit from deviation on ER (left) and
- Illustration of A(x), B(x), C(x), and D(x)
