arXiv subjects

Burkhard C. Schipper

Publications and source records attributed to Burkhard C. Schipper.

At least 19 recordsLinked to original sources

arXiv2026

Raising Bidders' Awareness in Second-Price Auctions

When bidders bid on complex objects, they might be unaware of characteristics affecting their valuations. We assume that each buyer's valuation is a sum of independent random variables, one for each characteristic. When a bidder is unaware of a characteristic, he omits the random variable from the sum. We study the seller's decision to raise bidders' awareness of characteristics before a second-price auction with entry fees. Optimal entry fees capture an additional unawareness rent due to unaware bidders misperceiving their probability of winning and the price to be paid upon winning. When raising a bidder's individual awareness of a characteristic with positive expected value, the seller faces a trade-off between positive effects on the expected first order statistic and unawareness rents of remaining unaware bidders on one hand and the loss of the unawareness rent from the newly aware bidder on the other. We present results on raising public awareness together with no versus full information. We discuss the winner's curse due to unawareness of characteristics.

econ.TH↗

arXiv2026

Conditional dominance in games with unawareness

Heifetz, Meier, and Schipper (2013) introduced dynamic game with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form associated with a dynamic game with unawareness consists of a partially ordered set of games in norm form. We use the generalized normal form to characterize extensive-form rationalizability (resp., prudent rationalizability) in dynamic games with unawareness by iterated conditional strict (resp., weak) dominance in the associated generalized normal form. We also show that the analogue to iterated admissibility for dynamic games with unawareness depends on extensive-form structure. This is because under unawareness, a player's information set not only determines which nodes she considers possible but also of which game tree(s) she is aware of.

cs.GT↗

arXiv2026

Kuhn's Theorem for Games of the Extensive Form with Unawareness

We extend Kuhn's Theorem to games of the extensive form with unawareness. We prove that if a game of the extensive form with unawareness has perfect recall, then for each mixed strategy there is an equivalent behavior strategy. We show that the converse does not hold under unawareness without restricting the evolution of the player's awareness to constant awareness along paths of play. Both directions of Kuhn's Theorem for games of the extensive form with unawareness require a condition complementary to perfect recall that rules out falsely believing in some events when the player is unaware of the actual past events.

econ.TH↗

arXiv2025

Mechanism Design under Unawareness -- Extended Abstract

We study the design of mechanisms under asymmetric awareness and information. While the mechanism designer cannot necessarily commit to a particular social choice function in the face of unawareness, she can at least commit to properties of social choice functions such as efficiency given ex post awareness. Assuming quasi-linear utilities and private values, we show that we can implement in conditional dominant strategies a social choice function that is utilitarian ex post efficient under pooled awareness without the need of the social planner being fully aware ex ante. To this end, we develop novel dynamic versions of Vickrey-Clarke-Groves mechanisms in which true types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. We show that ex ante unforeseen contingencies are no excuse for deficits. Finally, we propose a dynamic elaboration reverse second price auction for efficient procurement of complex incompletely specified projects with budget balance and participation constraints.

cs.GT↗

arXiv2025

Rationalizable Screening and Disclosure under Unawareness

We analyze a principal-agent procurement problem in which the principal (she) is unaware some of the marginal cost types of the agent (he). Communication arises naturally as some types of the agent may have an incentive to raise the principal's awareness (totally or partially) before a contract menu is offered. The resulting menu must not only reflect the principal's change in awareness, but also her learning about types from the agent's decision to raise her awareness in the first place. We capture this reasoning in a discrete concave model via a rationalizability procedure in which marginal beliefs over types are restricted to log-concavity, ``reverse'' Bayesianism, and mild assumptions of caution. We show that if the principal is ex ante only unaware of high-cost types, all of these types have an incentive raise her awareness of them -- otherwise, they would not be served. With three types, the two lower-cost types that the principal is initially aware of also want to raise her awareness of the high-cost type: Their quantities suffer no additional distortions and they both earn an extra information rent. Intuitively, the presence of an even higher cost type makes the original two look better. With more than three types, we show that this intuition may break down for types of whom the principal is initially aware of so that raising the principal's awareness could cease to be profitable for those types. When the principal is ex ante only unaware of more efficient (low-cost) types, then \textit{no type} raises her awareness, leaving her none the wiser.

econ.TH↗

arXiv2025

Discrete Screening

We consider a principal who wishes to screen an agent with \emph{discrete} types by offering a menu of \emph{discrete} quantities and \emph{discrete} transfers. We assume that the principal's valuation is discrete strictly concave and use a discrete first-order approach. We model the agent's cost types as non-integer, with integer types as a limit case. Our modeling of cost types allows us to replicate the typical constraint-simplification results and thus to emulate the well-treaded steps of screening under a continuum of contracts. We show that the solutions to the discrete F.O.C.s need not be unique \textit{even under discrete strict concavity}, but we also show that there cannot be more than two optimal contract quantities for each type, and that -- if there are two -- they must be adjacent. Moreover, we can only ensure weak monotonicity of the quantities \textit{even if virtual costs are strictly monotone}, unless we limit the ``degree of concavity'' of the principal's utility. Our discrete screening approach facilitates the use of rationalizability to solve the screening problem. We introduce a rationalizability notion featuring robustness with respect to an open set of beliefs over types called \textit{$Δ$-O Rationalizability}, and show that the set of $Δ$-O rationalizable menus coincides with the set of usual optimal contracts -- possibly augmented to include irrelevant contracts.

econ.TH↗

arXiv2025

Matching, Unanticipated Experiences, Divorce, Flirting, Rematching, Etc

We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market. Consequently, they may get ``divorced'' and rematch again with other agents, which may lead to further unanticipated experiences etc. A matching is stable if there is absence of pairwise common belief in blocking. Stable matchings can be destabilized by unanticipated experiences. Yet, we show that there exist self-confirming outcomes that are stable and do not lead to further unanticipated experiences. We introduce a natural decentralized matching process that, at each period assigns probability $1 - \varepsilon$ to the satisfaction of a mutual optimal blocking pair (if it exists) and picks any optimal blocking pair otherwise. The parameter $\varepsilon$ is interpreted as a friction of the matching market. We show that for any decentralized matching process, frictions are necessary for convergence to stability even without unawareness. Our process converges to self-confirming stable outcomes. Further, we allow for bilateral communication/flirting that changes the awareness and say that a matching is flirt-proof stable if there is absence of communication leading to pairwise common belief in blocking. We show that our natural decentralized matching process converges to flirt-proof self-confirming outcomes.

econ.TH↗

arXiv2025

Efficient Mechanisms under Unawareness

We study the design of efficient mechanisms under asymmetric awareness and information. Unawareness refers to the lack of conception rather than the lack of information. Assuming quasi-linear utilities and private values, we show that we can implement in conditional dominant strategies a social choice function that is utilitarian ex-post efficient when pooling all awareness of all agents without the need of the social planner being fully aware ex-ante. To this end, we develop novel dynamic versions of Vickrey-Clarke-Groves mechanisms in which types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. We show that ex-ante unforeseen contingencies are no excuse for deficits. Finally, we propose a modified reverse second price auction for efficient procurement of complex incompletely specified projects.

econ.TH↗

arXiv2025

Predicting the Unpredictable under Subjective Expected Utility

We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be known objects. Conditional on any sampled objects, she can also form beliefs about the next object being novel or being one of the previously sampled objects. We characterize behaviorally such beliefs under subjective expected utility. In doing so, we relate "reverse" Bayesianism, a central property in the literature on decision making under growing awareness, with exchangeable random partitions, the central property in the literature on the discovery of species problem and mutations in statistics, combinatorial probability theory, and population genetics. Partition exchangeable beliefs do not necessarily satisfy "reverse" Bayesianism. Yet, the most prominent models of exchangeable random partitions, the model by De Morgan (1838), the one parameter model of Ewens (1972), and the two parameter model of Pitman (1995) and Zabell (1997), do satisfy "reverse" Bayesianism. Our characterization allows us to interpret these models as subjective beliefs of a decision maker and to derive the parameters from choice behavior.

econ.TH↗

arXiv2024

Implicit Knowledge in Unawareness Structures

Awareness structures by Fagin and Halpern (1988) (FH) feature a syntactic awareness correspondence and accessibility relations modeling implicit knowledge. They are a flexible model of unawareness, and best interpreted from a outside modeler's perspective. Unawareness structures by Heifetz, Meier, and Schipper (2006, 2008) (HMS) model awareness by a lattice of state spaces and explicit knowledge via possibility correspondences. Sublattices thereof can be interpreted as subjective views of agents. Open questions include (1) how implicit knowledge can be defined in HMS structures, and (2) in which way FH structures can be extended to model the agents' subjective views. In this paper, we address (1) by defining implicit knowledge such that it is consistent with explicit knowledge in HMS models. We also introduce a variant of HMS models that instead of explicit knowledge, takes implicit knowledge and awareness as primitives. Further, we address (2) by introducing a category of FH models that are modally equivalent relative to sublanguages and can be interpreted as agents' subjective views depending on their awareness. These constructions allow us to show an equivalence between HMS and FH models. As a corollary, we obtain soundness and completeness of HMS models with respect to the Logic of Propositional Awareness, based on a language featuring both implicit and explicit knowledge.

cs.LO↗

arXiv2024

Level-k Thinking in the Extensive Form

Level-k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. Player's may learn about levels of opponents' thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l < k to her opponents consistent with the information set. We compare our notion of strong level-k thinking with other solution concepts such as level-k thinking in the associated normal form, strong rationalizability, Delta-rationalizability, iterated admissibility, backward rationalizability, backward level-k thinking, and backward induction. We use strong level-k thinking to reanalyze data from some prior experiments in the literature.

cs.GT↗

arXiv2023

Implicit Knowledge in Unawareness Structures -- Extended Abstract

Awareness structures by Fagin and Halpern (1988) (FH) feature a syntactic awareness correspondence and accessibility relations modeling implicit knowledge. They are a flexible model of unawareness, and best interpreted from a outside modeler's perspective. Unawareness structures by Heifetz, Meier, and Schipper (2006, 2008) (HMS) model awareness by a lattice of state-spaces and explicit knowledge via a possibility correspondence. They can be interpreted as providing the subjective views of agents. Open questions include (1) how implicit knowledge can be defined in HMS structures, and (2) in which way FH structures can be extended to model the agents' subjective views. In this paper, we address (1) by showing how to derive implicit knowledge from explicit knowledge in HMS models. We also introduce a variant of HMS models that instead of explicit knowledge, takes implicit knowledge and awareness as primitives. Further, we address (2) by introducing a category of FH models that are modally equivalent relative to sublanguages and can be interpreted as agents' subjective views depending on their awareness. These constructions allow us to show an equivalence between HMS and FH models. As a corollary, we obtain soundness and completeness of HMS models with respect to the Logic of Propositional Awareness, based on a language featuring both implicit and explicit knowledge.

cs.LO↗

arXiv2017

Self-confirming Games: Unawareness, Discovery, and Equilibrium

Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are "self-destroying" as a player's representation of the game must change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form games with unawareness in which players are now aware of actions that they have previously discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses an extensive-form rationalizable self-confirming equilibrium. This notion of equilibrium can be interpreted as steady-state of a learning and discovery process.

cs.GT↗

arXiv2015

Strategic Teaching and Learning in Games

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be evolutionary stable or that could "learn itself". Rather, a player has an incentive to strategically teach such a learning opponent in order secure at least the Stackelberg leader payoff. The impossibility result remains intact when restricted to the classes of generic games, two-player games, potential games, games with strategic complements or 2x2 games, in which learning is known to be "nice". More generally, it also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizable outcomes, iterated admissible outcomes, or minimal curb sets. A possibility result restricted to "strategically trivial" games fails if some generic games outside this class are considered as well.

cs.GT↗

arXiv2013

TARK 2013 - Proceedings of the 14. Conference on Theoretical Aspects of Rationality and Knowledge

The biannual TARK conferences bring together researchers from a wide variety of fields sharing a common interest in reasoning about rationality and knowledge. The impact of this tradition, going back to 1986, is apparent in many of today's research trends and in the growth of an intellectual community beyond traditional disciplinary boundaries. This volume documents the 14th TARK conference, held at the Institute of Mathematical Sciences, Chennai, India on January 7 to 9, 2013. It includes 18 contributed talks, 8 poster presentations, and 3 invited talks given at the conference. Like earlier volumes in this series, it gives a sense of the state of the art in studies of knowledge and rationality in areas such as game theory, decision theory, belief revision, language analysis, and computation. It should be of value to researchers, teachers, and students.

cs.GT↗

arXiv2013

Preference-Based Unawareness

Morris (1996, 1997) introduced preference-based definitions of knowledge and belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is characterized behaviorally as the event being null and its negation being null.

cs.GT↗

arXiv2013

When is tit-for-tat unbeatable?

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

cs.GT↗

arXiv2010

Pure Saddle Points and Symmetric Relative Payoff Games

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.

cs.GT↗