Model checking for coalition announcement logic

This talk is based on joint work with Rustam Galimullin and Hans van Ditmarsh, published in the German Conference on Artificial Intelligence (KI 2018). First I will introduce background and motivation for the work. I will introduce multi-agent Epistemic Logic (EL) for representing knowledge of (idealised) agents, Public Announcement Logic (PAL) for modelling knowledge change after truthful announcements, Group Announcement Logic (GAL) for modelling what kinds of changes in other agents’ knowledge a group of agents can effect, and Coalition Announcement Logic (CAL) which is the main subject of the talk. CAL studies how a group of agents can enforce a certain outcome by making a joint announcement, regardless of any announcements made simultaneously by the opponents. The logic is useful to model imperfect information games with simultaneous moves. It is also useful for devising protocols of announcements that will increase some knowledge of some agents, but also preserve other agents’ ignorance with respect to some information (in other words, preserve privacy of the announcers). The main new technical result in the talk is a model checking algorithm for CAL, that is, an algorithm for evaluating a CAL formula in a given finite model. The model-checking problem for CAL is PSPACE-complete, and the protocol requires polynomial space (but exponential time). DOI: 10.21146/2074-1472-2018-24-2-59-69

The combinatorics of CAT(0) cubical complexes

International audience Given a reconfigurable system $X$, such as a robot moving on a grid or a set of particles traversing a graph without colliding, the possible positions of $X$ naturally form a cubical complex $\mathcal{S}(X)$. When $\mathcal{S}(X)$ is a CAT(0) space, we can explicitly construct the shortest path between any two points, for any of the four most natural metrics: distance, time, number of moves, and number of steps of simultaneous moves. CAT(0) cubical complexes are in correspondence with posets with inconsistent pairs (PIPs), so we can prove that a state complex $\mathcal{S}(X)$ is CAT(0) by identifying the corresponding PIP. We illustrate this very general strategy with one known and one new example: Abrams and Ghrist's ``positive robotic arm" on a square grid, and the robotic arm in a strip. We then use the PIP as a combinatorial ``remote control" to move these robots efficiently from one position to another.

Carbon leakage: the role of sequential policy setting

We analyze non-cooperative environmental policy when the only strategic interaction between countries is through bilateral transboundary pollution, i.e., countries are closed or small open economies. Under simultaneous moves, there is no carbon leakage. However, in the sequential-move game, carbon leakage occurs; the leader sets its pollution tax lower than that in the simultaneous-move game and lower than the marginal damage from own pollution, while the follower sets its tax higher than that in the simultaneous-move game. The only motive behind the leader's underregulation of own pollution is to reduce the incidence of transboundary pollution from the follower. If pollution is a pure global public bad, aggregate pollution is higher in the sequential-move game than in the simultaneous-move game. The leader (follower) obtains higher (lower) welfare than that under simultaneous moves. Hence, if countries can choose to be leaders or followers, they choose to move first to set environmental taxes.

REFINEMENTS OF NASH EQUILIBRIA IN VIEW OF JEALOUS OR FRIENDLY BEHAVIOR OF PLAYERS

In this paper, several bargaining models, differing in some assumptions from each other, are analyzed. We consider a discrete case and a continuous case. In the former model, players bargain over a division of n objects. In the latter, parties divide one unit of infinitely divisible good. We start with an analysis of the one-round model, and then we consider a model in which players can continue to bargain. For each model, simultaneous moves as well as alternating offers of players are considered. The assumption that each player receives no more than his/her opponent proposes giving to him/her is the common assumption for all cases analyzed. Moreover, we adopt some assumptions concerning players' attitudes towards their opponents' payments, assuming that players can be either jealous or friendly. In view of the jealousy or friendliness of players, Nash equilibrium and subgame perfect equilibrium are described.

DEMAND-INDUCED ENDOGENOUS PRICE LEADERSHIP

This paper provides general conditions on the direct demand functions in a Bertrand duopoly with differentiated substitute products and constant marginal costs, that allow an unambiguous ranking of firms' equilibrium payoffs between sequential play (with both order of moves) on the one hand, and simultaneous play on the other. The main results are that (i) when prices are strategic complements, both firms prefer sequential moves (with either order) to simultaneous moves, (ii) when prices are strategic substitutes, both firms prefer simultaneous moves to moving second in sequential play, and (iii) in the mixed strategic substitute/complement case, one firm is as in (i) and the other as in (ii). Thus, sequential moves would plausibly endogenously emerge in cases (i) and (iii), with one specified leader in the latter case. The analysis relies crucially on the theory of supermodular games, and is conducted at a high level of generality, dispensing with concavity-type assumptions, and taking into account both the issues of existence and possible non-uniqueness of the different equilibria involved.