Research Interests
My current research interests lie in various applications of game theory. I am interested in mutual-choice matching problems (male-female, employer-employee) and in models of candidate selection for jobs by a committee. I have a long term interest in the field of search games, where players want to find each other (rendezvous search) or where one player wants to find an adversarial hider. The later relates to the general area of network search. The 'hider' could be an unknown economic variable such as future demand. A related area is that of patrolling a network against attack from an adversary, a new area known as 'patrolling games'.
I am also interested in 'caching games', where an agent caches material (squirrels hide nuts; terrorists, weapons; investors, money) some of which may be confiscated (or lost due to bank failures). The aim is to maximize the probability of having sufficient material left after loss (enough to survive the winter, to retire on).
Teaching in 2016-2017
Undergraduate
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IB4030: MMORSE - Dissertation
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IB3J30: Mathematical Game Theory: Combinatorial and Search Games
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IB2070: Mathematical Programming 2
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IB1040: Mathematical Programming I
Biography
I have recently joined the ORMS group at WBS after a long stay at the London School of Economics, where I was Professor of Mathematics and Operational Research. I grew up and completed my education in America, where I did my AB at Princeton (I wrote my Senior Thesis with Oskar Morgenstern) and my PhD at the Courant Institue-NYU (thesis on dynamical systems, under Peter Lax). I worked in America for a while before crossing the Atlantic, teaching at NYU, UCLA, Bryn Mawr and Yale.
I did much of my early work in the area of ergodic theory and dynamical systems, working with J. Oxtoby, S. Kakutani and V. Prasad. My more recent and current research interests are in the Operational Research areas of game theory, search theory (particularly rendezvous search, which I first proposed in 1976) and decentralized matching theory. Lately I have been applying theoretical results in search theory to animal behaviour (predator search for prey, 'pilferer' search for cached nuts). I have recently become interested in problems of group decision making, including jury voting and committees.
Publications
Journal Articles
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Alpern, S. and Baston, V. J. (2016) "The secretary problem with a selection committee : do conformist committees hire better secretaries", Management Science
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Papadaki, K., Alpern, S., Lidbetter, T. and Morton, A. (2016) "Patrolling a border", Operations Research
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Alpern, S., Fokkink, R. and Simanjuntak, M. (2016) "Optimal search and ambush for a hider who can escape the search region", European Journal of Operational Research, 251, 3, 707-714
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Alpern, S. and Chen, B. (2016) "The importance of voting order for decisions by sequential majority voting", European Journal of Operational Research
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Alpern, S., Auslander, J. and Silva, C. E. (2016) "The mathematical work of John Oxtoby", Contemporary Mathematics
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Alpern, S. and Lidbetter, T. (2015) "Optimal trade-off between speed and acuity when searching for a small object", Operations Research, 63, 1, 122-133
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Gal, S., Alpern, S. and Casas, J. (2015) "Prey should hide more randomly when a predator attacks more persistently", Journal of The Royal Society Interface, 12, 113, 20150861
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Alpern, S., Katrantzi, I. and Ramsey, D. (2014) "Equilibrium population dynamics when mating is by mutual choice based on age", Theoretical Population Biology, 94, 63-72
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Alpern, S. and Fokkink, R. (2014) "Accumulation games on graphs", Networks, Volume 64, Number 1, 40-47
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Alpern, S. and Lidbetter, T. (2014) "Searching a variable speed network", Mathematics of Operations Research, Volume 39, Number 3, 697-711
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Alpern, S., Katrantzi, I. and Ramsey, D. (2013) "Partnership formation with age-dependent preferences", European Journal of Operational Research, Vol.225, No.1, 91-99
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Alpern, S. and Lidbetter, T. (2013) "Mining coal or finding terrorists : the expanding search paradigm", Operations Research, 61, 2, 265-279
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Alpern, S. and Fokkink, R. (2013) "Illuminating a network from its nodes", The American Mathematical Monthly, Volume 120, Number 4, 358-359
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Alpern, S., Fokkink, R., Gal, S. and Timmer, M. (2013) "On search games that include ambush", SIAM Journal on Control and Optimization, Volume 51, Number 6, 4544-4556
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Alpern, S., Fokkink, R. and Pelekis, C. (2012) "A proof of the Kikuta–Ruckle conjecture on cyclic caching of resources", Journal of Optimization Theory and Applications, Vol.153, No.3, 650-661
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Alpern, S., Fokkink, R., Lidbetter, T. and Clayton, N. S. (2012) "A search game model of the scatter hoarder's problem", Journal of The Royal Society Interface, 9, 70, 869-879
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Alpern, S., Fokkink, R., Timmer, M. and Casas, J. (2011) "Ambush frequency should increase over time during optimal predator search for prey", Journal of the Royal Society Interface, Vol.8, No.64, 1665-1672
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Steve Alpern (2011) "Find-and-fetch search on a tree", Operations Research, Vol.59, No.5, 1258-1268
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Alpern, S., Morton, A. and Papadaki, K. (2011) "Patrolling Games", Operations Research, 59, 5, 1246-1257
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Steve Alpern (2011) "A new approach to Gal’s Theory of Search Games on Weakly Eulerian networks", Dynamic Games and Applications, 1, 2, 209-219
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Alpern, S., Fokkink, R. and Kikuta, K. (2010) "On Ruckle's conjecture on accumulation games", SIAM Journal on Control and Optimization, Vol.48, No.8, 5073-5083
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Alpern, S., Gal, S. and Solan, E. (2010) "A sequential selection game with vetoes", Games and Economic Behavior, Vol.68, No.1, 1-14
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Steve Alpern (2010) "Search games on trees with asymmetric travel times", SIAM Journal on Control and Optimization, Vol.48, No.8, 5547-5563
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Alpern, S., Fokkink, R. and Kikuta, K. (2010) "On Ruckle's Conjecture on Accumulation Games", SIAM Journal on Control and Optimization, 48, 8, 5073-5083
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Alpern, S. and Gal, S. (2009) "Analysis and design of selection committees : a game theoretic secretary problem", International Journal of Game Theory, Vol.38, No.3, 377-394
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Alpern, S., Baston, V. and Gal, S. (2009) "Searching symmetric networks with Utilitarian-Postman paths", Networks, Vol.53, No.4, 392-402
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Alpern, S. and Katrantzi, I. (2009) "Equilibria of two-sided matching games with common preferences", European Journal of Operational Research, Vol.196, No.3, 1214-1222
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Steve Alpern (2008) "Line-of-sight rendezvous", European Journal of Operational Research, Vol.188, No.3, 865-883
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Steve Alpern (2008) "Hide-and-seek games on a tree to which Eulerian networks are attached", Networks, Vol.52, No.3, 162-166
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Alpern, S., Fokkink, R., Lindelauf, R. and Olsder, G. (2008) "The “Princess and Monster” game on an interval", SIAM Journal on Control and Optimization, Vol.47, No.3, 1178-1190
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Alpern, S., Baston, V. and Gal, S. (2008) "Network search games with immobile hider, without a designated searcher starting point", International Journal of Game Theory, 37, 2, 281-302
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Alpern, S. and Prasad, V. (2008) "MultiTowers, conjugacies and codes : three theorems in ergodic theory, one variation on Rokhlin's Lemma", Proceedings of the Mathematical Society, Vol.136, No.12, 4373-4383
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Alpern, S. and Prasad, V. (2007) "Rotational (and other) representations of stochastic matrices", Stochastic Analysis and Applications, Vol.26, No.1, 1-15
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Steve Alpern (2007) "Rendezvous Search with Revealed Information : Applications to the Line
", Journal of Applied Probability, 44, 1, 1-15
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Alpern, S. and Baston, V. (2006) "Rendezvous in Higher Dimensions", SIAM Journal on Control and Optimization, 44, 6, 2233-2252
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Alpern, S. and Baston, V. (2006) "A common notion of clockwise can help in planar rendezvous", European Journal of Operational Research, 175, 2, 688-706
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Alpern, S. and Baston, V. (2005) "Rendezvous on a Planar Lattice", Operations Research, 53, 6, 996-1006
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Alpern, S. and Reyniers, D. (2005) "Strategic mating with common preferences", Journal of Theoretical Biology, 237, 4, 337-354
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Alpern, S. and Gal, S. (2002) "Searching for an Agent Who May OR May Not Want to be Found", Operations Research, 50, 2, 311-323
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Alpern, S. and Reyniers, D. J. (2002) "Spatial dispersion as a dynamic coordination problem
", Theory and Decision, 53, 1, 29-59
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Alpern, S. and Lim, W. S. (2002) "Rendezvous of three agents on the line", Naval Research Logistics, 49, 3, 244-255
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Steve Alpern (2002) "Rendezvous search on labeled networks", Naval Research Logistics, 49, 3, 256-274
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Steve Alpern (2002) "Rendezvous Search : A Personal Perspective", Operations Research, 50, 5, 772-795
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Alpern, S. and Prasad, V. (2002) "Properties generic for Lebesgue space automorphisms are generic for measure-preserving manifold homeomorphisms", Ergodic Theory and Dynamical Systems, 22, 06, 1587-1620
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Alpern, S. and Reyniers, D. (2001) "Games of crowding
", International Game Theory Review, 03, 01, 27-56
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Alpern, S. and Beck, A. (2000) "Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance", Operations Research, 48, 3, 498-501
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Alpern, S. and Prasad, V. (2000) "Maximally chaotic homeomorphisms of sigma-compact manifolds", Topology and its Applications, 105, 1, 103-112
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Alpern, S. and Reyniers, D. (1999) "Strategic Mating with Homotypic Preferences", Journal of Theoretical Biology, 198, 1, 71-88
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Steve Alpern (1999) "Combinatorial approximation by Devaney-chaotic or periodic volume preserving homeomorphisms
", International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 9, 5, 843-848
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Alpern, S. and Beck, A. (1999) "Asymmetric Rendezvous on the Line Is a Double Linear Search Problem", Mathematics of Operations Research, 24, 3, 604-618
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Alpern, S. and Beck, A. (1999) "Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting", Operations Research, 47, 6, 849 -861
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Alpern, S., Baston, V. J. and Essegaier, S. (1999) "Rendezvous search on a graph
", Journal of Applied Probability, 36, 1, 223-231
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Alpern, S. and Prasad, V. (1999) "Chaotic homeomorphisms of R^n, lifted from torus homeomorphisms
", Topology and its Applications, 105, 1, 103-112
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Alpern, S. and Lim, W. S. (1998) "The Symmetric Rendezvous-Evasion Game", SIAM Journal on Control and Optimization, 36, 3, 948-959
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Alpern, S. and Beck, A. (1997) "Rendezvous search on the line with bounded resources: expected time minimization", European Journal of Operational Research, 101, 3, 588-597
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Lim, W. S., Alpern, S. and Beck, A. (1997) "Rendezvous search on the line with more than two players", Operations Research, 45, 3, 357-364
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Lim, W. S. and Alpern, S. (1996) "Minimax Rendezvous on the Line", SIAM Journal on Control and Optimization, 34, 5, 1650-1665
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Steve Alpern (1995) "Almost Periodic Ergodic Rn-Homeomorphisms", Advances in Mathematics, 116, 1, 46-54
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Alpern, S. and Gal, S. (1995) "Rendezvous Search on the Line with Distinguishable Players", SIAM Journal on Control and Optimization, 33, 4, 1270-1276
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Steve Alpern (1995) "The Rendezvous Search Problem", SIAM Journal on Control and Optimization, 33, 3, 673-683
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Alpern, S. and Prasad, V. (1995) "Typical Transitivity for Lifts of Rotationless Annulus or Torus Homeomorphisms", Bulletin of the London Mathematical Society, 27, 1, 79-81
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Alpern, S. and Prasad, V. (1993) "Combinatorial Proofs of the Conley-Zehnder-Franks Theorem on a Fixed Point for Torus Homeomorphisms", Advances in Mathematics, 99, 2, 238-247
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Alpern, S. and Prasad, V. (1993) "Combinatorial Proofs of the Conley-Zehnder-Franks Theorem on a Fixed Point for Torus Homeomorphisms", Advances in Mathematics, 99, 2, 238-247
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Alpern, S. and Prasad, V. (1993) "Topological ergodic theory and mean rotation
", Proceedings of the American Mathematical Society, 118, 1, 279-284
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Steve Alpern (1992) "Infiltration games on arbitrary graphs", Journal of Mathematical Analysis and Applications, 163, 1, 286-288
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Alpern, S. and Prasad, V. (1991) "Typical recurrence for lifts of mean rotation zero annulus homeomorphisms", Bulletin of the London Mathematical Society, 23, 5, 477-481
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Steve Alpern (1991) "Cycles in extensive form perfect information games", Journal of Mathematical Analysis and Applications, 159, 1, 1-17
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Alpern, S. and Beck, A. (1991) "Hex games and twist maps on the annulus", The American Mathematical Monthly, 98, 9, 803-811
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Alpern, S. and Prasad, V. (1990) "Return times for nonsingular measurable transformations", Journal of Mathematical Analysis and Applications, 152, 2, 470-487
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Steve Alpern (1989) "Geometric search theory and demand uncertainty", Engineering Costs and Production Economics, 17, 1-4, 245-251
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Alpern, S. and Prasad, V. (1989) "Coding a Stationary Process to One with Prescribed Marginals", The Annals of Probability, 17, 4, 1658-1663
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Alpern, S. and Snower, D. J. (1989) "A search model of optimal pricing and production", Engineering Costs and Production Economics, 15, 279-284
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Alpern, S. and Gal, S. (1988) "A Mixed-Strategy Minimax Theorem without Compactness", SIAM Journal on Control and Optimization, 26, 6, 1357-1361
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Alpern, S., Choksi, J. R. and Prasad, V. (1988) "Conjugates of infinite measure preserving transformations", Canadian Journal of Mathematics, 40, 3, 742-749
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Steve Alpern (1988) "Game with repeated decisions", SIAM Journal on Control and Optimization, 26, 2, 468-477
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Alpern, S. and Snower, D. J. (1988) "'High-low search' in product and labor markets", The American Economic Review, 78, 2, 356-362
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Alpern, S. and Prasad, V. (1988) "Dynamics induced on the ends of non-compact manifold", Ergodic Theory and Dynamical Systems, 8, 01, 1-15
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Steve Alpern (1988) "Area preserving homeomorphisms of the open disk without fixed points
", Proceedings of the American Mathematical Society, 103, 2, 624-626
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Alpern, S. and Prasad, V. (1987) "End behaviour and ergodicity for homeomorphisms of manifolds with finitely many ends", Canadian Journal of Mathematics, 39, 2, 473-491
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Alpern, S. and Prasad, V. (1987) "Weak mixing manifold homeomorphisms preserving an infinite measure
", Canadian Journal of Mathematics, 39, 6, 1475-1488
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Alpern, S. and Ašić, M. D. (1986) "Search Games (Shmuel Gal)", SIAM Review, 24, 2, 235-236
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Alpern, S. and Asic, M. (1986) "Ambush Strategies in Search Games on Graphs", SIAM Journal on Control and Optimization, 24, 1, 66-75
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Steve Alpern (1985) "Search for point in interval, with high–low feedback", Mathematical Proceedings of the Cambridge Philosophical Society, 98, 3, 569-578
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Alpern, S. and Asic, M. (1985) "The search value of a network", Networks, 15, 2, 229-238
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Steve Alpern (1985) "Conjecture: In General a Mixing Transformation is Not Two-Fold Mixing", The Annals of Probability, 13, 1, 310-313
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Steve Alpern (1983) "Rotational representations of stochastic matrices
", Annals of Probability, 11, 3, 789-794
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Steve Alpern (1983) "Nonstable Ergodic Homeomorphisms of R^4", Indiana University Mathematics Journal, 32, 187-191
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Steve Alpern (1981) "Return times and conjugates of an antiperiodic transformation", Ergodic Theory and Dynamical Systems, 1, 02, 135-143
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Steve Alpern (1979) "Measure preserving Homeomorphisms of R^n", Indiana University Mathematics Journal, 28, 957-960
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Alpern, S. and Edwards, R. D. (1979) "Lusin's theorem for measure preserving homeomorphisms", Mathematika, 26, 1, 33-43
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Steve Alpern (1978) "Superhamiltonian graphs", Journal of Combinatorial Theory, Series B, 25, 1, 62-73
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Steve Alpern (1978) "Approximation to and by measure preserving homeomorphisms", Journal of the London Mathematical Society, s2-18, 2, 305-315
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Steve Alpern (1978) "A topological analog of Halmos' conjugacy lemma", Inventiones Mathematicae, 48, 1, 1-6
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Steve Alpern (1976) "New proofs that weak mixing is generic", Inventiones Mathematicae, 32, 3, 263-278
Book Items
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Alpern, S. and Fokkink, R. (2010) "Disperse or unite? A mathematical model of coordinated attack", 6442, 220, Springer, London
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Alpern, S., Fokkink, R., Lindelauf, R. and Olsder, G. (2009) "A numerical approach to the ‘Princess and Monster’ game on an interval
", 10, 149, Springer [distributor], Boston, Mass. : Birkhäuser ; London