Good-for-games $\omega$-Pushdown Automata

We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are that $\omega$-GFG-PDA are more expressive than deterministic $\omega$- pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite.

Nonadditive integration and some solutions of cooperative games

In the paper, we propose three schemes of nonadditive integration based on several extensions of nonadditive set function and integrand to the appropriate symmetric power of the original measurable space. A survey on the integral representation of some classic objects of the cooperative game theory, derived by nonadditive integration, is given. A universal approach for investigation of both finite and infinite games is developed. We pay a particular attention to the Shapley value, Owen multilinear extension, and support function of the core of a convex cooperative game.

Capital Allocation Rules and the No-Undercut Property

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures.

It's about time

PurposeTime is a critical element of commercial real estate (CRE) and has received only cursory attention. This paper identifies and describes the interactions between time, change and CRE. It leads to important implications and possible changes in professional practice, teaching and research.Design/methodology/approachThe research design involves identifying and synthesising research in a disparate discipline into a coherent portrayal of time, change and CRE. Using the CRE environment as a foundation, a more comprehensive, multi-disciplinary approach is developed to highlight the temporal issues within CRE.FindingsThe extreme levels of complexity, dynamism and uncertainty characterising current CRE environments affect the interaction of time, change and CRE. In response, CRE has become increasingly specialised in property types and time segments. The paper identifies four issues for CRE: the role of CRE as an integrator of different layers of civilisation with different clock speeds, the need for a temporal mindset recognising finite and infinite games, the need for temporal ambidexterity and the use of strategic foresight and scenarios. The very definition of CRE as an industry is questioned.Research limitations/implicationsNeed for essential empirical work as well as additional work for implications.Practical implicationsCRE faces disruption from many sources, and this paper considers how to incorporate time and change into analysis of the CRE market environment. It identifies specific ways CRE can understand and avoid disruption. Further, areas of teaching and research are highlighted.Social implicationsReal estate assets are substantial, long-lived assets with important consequences for society. This paper advances the analysis of such assets.Originality/valueAreas of concentration in CRE and academia needing attention are identified. The areas have generally not been considered prior to this paper.