4 Presentations

• 
  02:00 PM - 02:25 PM

  On a large population game theoretic model of associative mating

  • David Ramsey, presenter, Wrocław University of Technology

  This presentation considers a model of partnership formation in a seasonally breeding population. Each member of a large population begins searching for a partner of the opposite sex at the same time. There are k classes of both males and females. Searchers prefer mates which are similar to themselves (e.g. the classes may represent different subspecies). Pairing only occurs by mutual consent. Each individual searches until a mutually acceptable partner is found and then both individuals leave the mating pool. Hence, the distribution of the classes changes as the mating season progresses, as well as the rate at which prospective partners are found. Conditions that an evolutionarily stable profile of strategies must satisfied are given. Examples of such games in which multiple equilibria exist are presented.

• 
  02:25 PM - 02:50 PM

  Evolution of Decisions in Population Games with Sequentially Searching Individuals

  • Tadeas Priklopil, presenter, University of Lausanne

  In many social situations, individuals endeavor to find the single best possible
  partner, but are constrained to evaluate the candidates in sequence. Examples include the
  search for mates, economic partnerships, or any other long-term ties where the choice
  to interact involves two parties. Surprisingly, however, previous theoretical work on
  mutual choice problems focuses on finding equilibrium solutions, while ignoring the
  evolutionary dynamics of decisions. Empirically, this may be of high importance, as
  some equilibrium solutions can never be reached unless the population undergoes radical
  changes and a sufficient number of individuals change their decisions simultaneously. To
  address this question, we apply a mutual choice sequential search problem in an evolutionary
  game-theoretical model that allows one to find solutions that are favored by evolution. As
  an example, we study the influence of sequential search on the evolutionary dynamics of
  cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma
  game.

• 
  02:50 PM - 03:15 PM

  Search-and-Rescue Rendezvous

  • Pierre Leone, presenter, University of Geneva
  • Steve Alpern, Warwick Business School

  We consider a new type of asymmetric rendezvous search problem in which Agent II needs to give Agent
  I a `gift' which can be in the form of information or material. The gift can either be transferred upon
  meeting, as in traditional rendezvous, or it can be dropped o by II at a location he passes, in the hope
  it will be found by I. The gift might be a water bottle for a traveler lost in the desert; a supply cache
  for Lieutenant Scott in the Antarctic; or important information (left as a gift). The common aim of
  the two agents is to minimize the time taken for I to either meet II or find the gift. We find optimal
  agent paths and dropping times when the search region is a line, the initial distance between the players
  is known and one or both of the players can leave gifts. When there are no gifts this is the classical
  asymmetric rendezvous problem solved by Alpern and Gal in 1995 (Alpern and Gal 1995). We exhibit
  strategies solving these various problems and use a `rendezvous algorithm' to establish their optimality.

• 
  03:15 PM - 03:40 PM

  Dynamic search for balls hidden in boxes

  • Thomas Lidbetter, presenter, Rutgers University
  • Kyle Lin, Naval Postgraduate School

  Many practical search problems concern the search for multiple hidden objects or
  agents, such as earthquake survivors. In such problems, knowing only the list of possible
  locations, the Searcher needs to find all the hidden objects by visiting these locations
  one by one. To study this problem, we formulate new game-theoretic models of discrete
  search between a Hider and a Searcher. The Hider hides k balls in n boxes, and the
  Searcher opens the boxes one by one with the aim of finding all the balls. Every time
  the Searcher opens a box she must pay its search cost, and she either finds one of the
  balls it contains or learns that it is empty. If the Hider is an adversary, an appropriate
  payoff function may be the expected total search cost paid to find all the balls, while if
  the Hider is Nature, a more appropriate payoff function may be the difference between
  the total amount paid and the amount the Searcher would have to pay if she knew
  the locations of the balls a priori (the regret). We give a full solution to the regret
  version of this game, and a partial solution to the search cost version. We also consider
  variations on these games for which the Hider can hide at most one ball in each box.
  The search cost version of this game has already been solved in previous work, and we
  give a partial solution in the regret version. This is joint work with Kyle Lin.