Search Games and Other Applications of Game Theory

Garnaev, Andrey

doi:10.1007/978-3-642-57304-0

Cited by 82 publications

(44 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternative approaches to the latter problem were given by Lalley & Robbins [8] and Garnaev [9]. Further work on related search games was carried out by Kikuta & Ruckle [10], Pavlovic [11] and Alpern et al [12] (see also the monographs [13,14]). …”

Section: Search Games With Mobile Hidermentioning

confidence: 99%

Ambush frequency should increase over time during optimal predator search for prey

Alpern

Fokkink

Timmer

et al. 2011

J. R. Soc. Interface.

View full text Add to dashboard Cite

We advance and apply the mathematical theory of search games to model the problem faced by a predator searching for prey. Two search modes are available: ambush and cruising search. Some species can adopt either mode, with their choice at a given time traditionally explained in terms of varying habitat and physiological conditions. We present an additional explanation of the observed predator alternation between these search modes, which is based on the dynamical nature of the search game they are playing: the possibility of ambush decreases the propensity of the prey to frequently change locations and thereby renders it more susceptible to the systematic cruising search portion of the strategy. This heuristic explanation is supported by showing that in a new idealized search game where the predator is allowed to ambush or search at any time, and the prey can change locations at intermittent times, optimal predator play requires an alternation (or mixture) over time of ambush and cruise search. Thus, our game is an extension of the well-studied 'Princess and Monster' search game. Search games are zero sum games, where the pay-off is the capture time and neither the Searcher nor the Hider knows the location of the other. We are able to determine the optimal mixture of the search modes when the predator uses a mixture which is constant over time, and also to determine how the mode mixture changes over time when dynamic strategies are allowed (the ambush probability increases over time). In particular, we establish the 'square root law of search predation': the optimal proportion of active search equals the square root of the fraction of the region that has not yet been explored.

show abstract

Section: Search Games With Mobile Hidermentioning

confidence: 99%

Ambush frequency should increase over time during optimal predator search for prey

Alpern

Fokkink

Timmer

et al. 2011

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…LetT = 5. Then, by Theorem 2 as the first step we calculate ϕ t for t ∈ [1,5]. In our case we get (0, 0.14, 0.616, 1.830, 4.581).…”

Section: Numerical Examplesmentioning

confidence: 88%

“…Let also g = 0.9,T 1 = 5,T 2 = 1. Then, by Theorem 6 as the first step we calculate ϕ 2 t for t ∈ [1,5] The equilibrium strategies of all three cases are shown in Figure 1. When a new user comes into competition, it leads to a bigger rivalry for using good quality channels and it results in the situation when bad quality channels turn out to become more attractive for users than they were when there were smaller number of users.…”

Section: Numerical Examplesmentioning

confidence: 99%

Closed Form Solutions for Symmetric Water Filling Games

Altman

Avrachenkov

Garnaev

2008

2008 Proceedings IEEE INFOCOM - The 27th Conference on Computer Communications

View full text Add to dashboard Cite

Abstract-We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multipliers. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the Iterative Water Filling Algorithm. Furthermore, it turns out that the convergence of Iterative Water Filling Algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.

show abstract

“…More applied work in this area has been carried out by Jotshi and Batta [16]. The topic of search games has been the subject of books by Gal [12], Alpern and Gal [6], and Garnaev [14].…”

Section: T (S; H)d(s H)mentioning

confidence: 99%

Searching a Variable Speed Network

Alpern¹,

Lidbetter

2014

Mathematics of OR

View full text Add to dashboard Cite

A point H lies on a network Q according to some unknown distribution. A Searcher starts at a given point O of Q and moves to …nd H at speeds which depend on his location and direction. He seeks the randomized search algorithm which minimizes the expected search time. This is equivalent to modeling the problem as a zero-sum hide-and-seek game whose value V is called the search value of (Q; O).We make a new and direct derivation of an explicit formula V = (1=2) ( + ) for the search value of a tree, where is the minimum tour time of Q and (called the incline of Q) is an average over the leaf nodes i of the di¤er-; where d (x; y) is the time to go from x to y: The function can be interpreted as height, assuming uphill is slower than downhill. We then apply this formula to obtain numerous results for general networks. We also introduce a new general method of comparing the search value of networks which di¤er in a single arc. Some simple networks have very complicated optimal strategies which require mixing of a continuum of pure strategies. Many of our results generalize analogous ones obtained for constant velocity (in both directions) by S. Gal, but not all of those results can be extended.

show abstract

Search Games and Other Applications of Game Theory

Abstract: Search games and other applications of game theory I Andrej Gamaev.

Cited by 82 publications

References 0 publications

Ambush frequency should increase over time during optimal predator search for prey

Ambush frequency should increase over time during optimal predator search for prey

Closed Form Solutions for Symmetric Water Filling Games

Searching a Variable Speed Network

Contact Info

Product

Resources

About