Potential Games

... Clearly, every maximum point S for F has to satisfy (2.13) and thus coincides with a (pure-strategy) Nash equilibrium for G . Note also that S can either be a local or a global optimum. The set of global maximizers for F therefore is a subset of NESet.G /. However, one may only consider these glob ...

... Clearly, every maximum point S for F has to satisfy (2.13) and thus coincides with a (pure-strategy) Nash equilibrium for G . Note also that S can either be a local or a global optimum. The set of global maximizers for F therefore is a subset of NESet.G /. However, one may only consider these glob ...

Defining Winning Strategies in Fixed-Point Logic

... are used to model reactive systems where the construction of winning strategies corresponds to the synthesis of controllers. Strategies can be viewed and presented in several different ways, and it is not always obvious what deﬁnability of strategies really means. However, for the games that we cons ...

... are used to model reactive systems where the construction of winning strategies corresponds to the synthesis of controllers. Strategies can be viewed and presented in several different ways, and it is not always obvious what deﬁnability of strategies really means. However, for the games that we cons ...

e-Consistent equilibrium in repeated games - IMJ-PRG

... converge to an equilibrium. Far enough in each one of these learning processes only e-equilibrium is achieved and not an exact equilibrium. In Kalai and Lehrer (1993), for instance, players gradually learn other players' strategies, but never get to fully know them. Thus, players optimize against st ...

... converge to an equilibrium. Far enough in each one of these learning processes only e-equilibrium is achieved and not an exact equilibrium. In Kalai and Lehrer (1993), for instance, players gradually learn other players' strategies, but never get to fully know them. Thus, players optimize against st ...

New complexity results about Nash equilibria

... A key concept in computational complexity theory is that of a reduction from one problem A to another problem B. Informally, a reduction maps every instance of computational problem A to a corresponding instance of computational problem B, in such a way that the answer to the former instance can be ...

... A key concept in computational complexity theory is that of a reduction from one problem A to another problem B. Informally, a reduction maps every instance of computational problem A to a corresponding instance of computational problem B, in such a way that the answer to the former instance can be ...

PDF

... identifying the equilibrium by method of triangulation. Much of the later research, such as the papers by van der Laan and Talman [28, 29, 30] and Doup and Talman [4, 5] have concentrated on making improvements on these Scarf algorithm. In terms of algorithms that can be used specifically for comput ...

... identifying the equilibrium by method of triangulation. Much of the later research, such as the papers by van der Laan and Talman [28, 29, 30] and Doup and Talman [4, 5] have concentrated on making improvements on these Scarf algorithm. In terms of algorithms that can be used specifically for comput ...

Existence of stationary equilibrium for mixtures of discounted

... with uncountable state space and show the existence of independent stationary equilibrium strategy for both players. Parthasarathy and Sinha21 further show the existence of stationary equilibrium strategies for non-zero sum discounted stochastic games with uncountable state space, finite action spac ...

... with uncountable state space and show the existence of independent stationary equilibrium strategy for both players. Parthasarathy and Sinha21 further show the existence of stationary equilibrium strategies for non-zero sum discounted stochastic games with uncountable state space, finite action spac ...

Delegating Decisions in Strategic Settings Sarit Kraus and Michael Wooldridge

... decisions whose outcome will affect us, even though we know full well that the agents we delegate the decisions to are self-interested, and will make these decisions in their own interest. For example, consider the chair of a university department, who must allocate teaching and admin responsibiliti ...

... decisions whose outcome will affect us, even though we know full well that the agents we delegate the decisions to are self-interested, and will make these decisions in their own interest. For example, consider the chair of a university department, who must allocate teaching and admin responsibiliti ...

Playing Games in Many Possible Worlds

... be applied to Socratic games with constant-sum (or strategically zero-sum) worlds. We face two major obstacles in extending these classical results to Socratic games. First, a Socratic game with constant-sum worlds is not itself a constant-sum classical game—rather, the resulting classical game is o ...

... be applied to Socratic games with constant-sum (or strategically zero-sum) worlds. We face two major obstacles in extending these classical results to Socratic games. First, a Socratic game with constant-sum worlds is not itself a constant-sum classical game—rather, the resulting classical game is o ...

16.410 Lecture 24: Sequential Games

... build the whole tree, find terminal states and evaluate the corresponding rewards; Moving backwards from the leaves, associate to parent nodes the MIN or MAX value of all their children (depending on whose turn it is). ...

... build the whole tree, find terminal states and evaluate the corresponding rewards; Moving backwards from the leaves, associate to parent nodes the MIN or MAX value of all their children (depending on whose turn it is). ...

Extensive Form Games and Subgame Perfection

... him(A, G) and (A, H), even though once A is chosen the G-versus-H choice is moot. The definition of best response and Nash equilibria in this game are exactly as they are in for normal form games. Indeed, this example illustrates how every perfectinformation game can be converted to an equivalent no ...

... him(A, G) and (A, H), even though once A is chosen the G-versus-H choice is moot. The definition of best response and Nash equilibria in this game are exactly as they are in for normal form games. Indeed, this example illustrates how every perfectinformation game can be converted to an equivalent no ...

Now It`s Personal: On Abusive Game Design

... implied player model suggests, always maintaining a desired and “positive” experience of the game. But where does this notion come from? Play theorist Bernard Suits writes on the notion of “the lusory attitude” [42], an active state of mind in which players try to uphold both the rules of a game and ...

... implied player model suggests, always maintaining a desired and “positive” experience of the game. But where does this notion come from? Play theorist Bernard Suits writes on the notion of “the lusory attitude” [42], an active state of mind in which players try to uphold both the rules of a game and ...

Backward Induction and Subgame Perfection

... Idea: some parts of the game tree can stand alone as a game. These are called subgames. Example: The game we considered, after Player 1 plays Bottom. De…nition: a node h’s successors are all the nodes after h, all the way to the terminal nodes (end of the game tree). De…nition: Suppose you have a ga ...

... Idea: some parts of the game tree can stand alone as a game. These are called subgames. Example: The game we considered, after Player 1 plays Bottom. De…nition: a node h’s successors are all the nodes after h, all the way to the terminal nodes (end of the game tree). De…nition: Suppose you have a ga ...

1 Sequential Games

... While there have been criteria used to eliminate Nash equilibria, this is the …rst major re…nement of the basic concept of Nash equilibrium that we have seen. While all subgame perfect Nash equilibria of a game are Nash equilibria, not all Nash equilibria are subgame perfect. This means that if you ...

... While there have been criteria used to eliminate Nash equilibria, this is the …rst major re…nement of the basic concept of Nash equilibrium that we have seen. While all subgame perfect Nash equilibria of a game are Nash equilibria, not all Nash equilibria are subgame perfect. This means that if you ...

Stochastic games of control and stopping for a linear diffusion

... In the first of our games, which is zero-sum, player A has a continuous reward function u : [0, 1] → R . In addition to α(·) , player A chooses a stopping rule τ and seeks to maximize the expectation of u(Xτ ) ; whereas player B chooses β(·) and aims to minimize this expectation. In the second game, ...

... In the first of our games, which is zero-sum, player A has a continuous reward function u : [0, 1] → R . In addition to α(·) , player A chooses a stopping rule τ and seeks to maximize the expectation of u(Xτ ) ; whereas player B chooses β(·) and aims to minimize this expectation. In the second game, ...

Families of semipermeable curves and their application to some

... 1. Semipermeable curves in the theory of antagonistic differential games are smooth curves in the plane that possess the property: the first player is able to prevent the trajectories of the controlled system from crossing the curve from one (positive) side to the other (negative) side, the second p ...

... 1. Semipermeable curves in the theory of antagonistic differential games are smooth curves in the plane that possess the property: the first player is able to prevent the trajectories of the controlled system from crossing the curve from one (positive) side to the other (negative) side, the second p ...

The Game World is Flat: The Complexity of Nash Equilibria in

... – network congestion games, where the strategies of each player are given implicitly as paths from a source to a sink in a graph; since the number of strategies is potentially exponential, this representation is not of polynomial type; we treat network congestion games in Section 4. – multimatrix ga ...

... – network congestion games, where the strategies of each player are given implicitly as paths from a source to a sink in a graph; since the number of strategies is potentially exponential, this representation is not of polynomial type; we treat network congestion games in Section 4. – multimatrix ga ...

Power indices expressed in terms of minimal winning coalitions

... A common point of the Shapley-Shubik and Banzhaf-Penrose measures is that they can be expressed in terms of marginal contributions of the players, which are weighted according to coefficients that depend on the measure not on the particular game at hand. This feature is shared by other semivalues: v ...

... A common point of the Shapley-Shubik and Banzhaf-Penrose measures is that they can be expressed in terms of marginal contributions of the players, which are weighted according to coefficients that depend on the measure not on the particular game at hand. This feature is shared by other semivalues: v ...

The position value is the Myerson value, in a sense

... Figure 2. The graph of a hyperlink agent form 2 who is the only player in G with more than one hyperlink is split into two agents, 2.1 and 2.2, which are (completely) connected by a link (dotted line); the other players are represented by a single agent, respectively. The representatives of h and h0 ...

... Figure 2. The graph of a hyperlink agent form 2 who is the only player in G with more than one hyperlink is split into two agents, 2.1 and 2.2, which are (completely) connected by a link (dotted line); the other players are represented by a single agent, respectively. The representatives of h and h0 ...

Two-Person Games with Unique Nash Equilibria

... class of games with unique Nash equilibria. We did not expect much as these conditions are rather simple, but to our surprise, our program returned a condition that is more general than the strict competitiveness condition. As it turned out, it exactly corresponds to Kats and Thisse’s [1992] class o ...

... class of games with unique Nash equilibria. We did not expect much as these conditions are rather simple, but to our surprise, our program returned a condition that is more general than the strict competitiveness condition. As it turned out, it exactly corresponds to Kats and Thisse’s [1992] class o ...

Sequential games - Moty Katzman`s Home Page

... either player I can choose a leaf with outcome in S or she is forced to choose a leaf with outcome not in S. Assume now that r > 1 and that the result holds for all games with trees of rank less than r . Let G1 , . . . , Gn be the subgames resulting after player I makes her move, and let T1 , . . . ...

... either player I can choose a leaf with outcome in S or she is forced to choose a leaf with outcome not in S. Assume now that r > 1 and that the result holds for all games with trees of rank less than r . Let G1 , . . . , Gn be the subgames resulting after player I makes her move, and let T1 , . . . ...

A Typology of Players: between Instinctive and Contemplative

... contemplative action. Thus, a player will be classified as type p if the probability of him choosing a contemplative action is p. The main body of the paper consists of identifying the typology for a specific dataset. The first part of the paper (Section 3) provides the groundwork for defining the t ...

... contemplative action. Thus, a player will be classified as type p if the probability of him choosing a contemplative action is p. The main body of the paper consists of identifying the typology for a specific dataset. The first part of the paper (Section 3) provides the groundwork for defining the t ...

(pdf)

... the first player who cannot make a move loses, the first player to go in this case loses, and the second player wins. In the case of the game with assigned value 1, we see that Left has a move, namely, to bring the game to the 0 game, while Right has no move. Right loses. It is the opposite in the g ...

... the first player who cannot make a move loses, the first player to go in this case loses, and the second player wins. In the case of the game with assigned value 1, we see that Left has a move, namely, to bring the game to the 0 game, while Right has no move. Right loses. It is the opposite in the g ...

Computing Stackelberg Strategies in Stochastic

... of the game, with the exception of player 2 learning player 1’s mixed strategy before acting. This includes work on computing Stackelberg mixed strategies in normalform games [Conitzer and Sandholm 2006; von Stengel and Zamir 2010; Conitzer and Korzhyk 2011], Bayesian games [Conitzer and Sandholm 20 ...

... of the game, with the exception of player 2 learning player 1’s mixed strategy before acting. This includes work on computing Stackelberg mixed strategies in normalform games [Conitzer and Sandholm 2006; von Stengel and Zamir 2010; Conitzer and Korzhyk 2011], Bayesian games [Conitzer and Sandholm 20 ...

The General Game Playing Description Language Is Universal

... With GDL the organisers of the AAAI GGP Competition sought a high-level game specification language that admits a purely declarative reading and thus allows general gameplaying systems to reason about the rules of a game. In this regard, GDL follows the tradition of AI Planning. Planning languages h ...

... With GDL the organisers of the AAAI GGP Competition sought a high-level game specification language that admits a purely declarative reading and thus allows general gameplaying systems to reason about the rules of a game. In this regard, GDL follows the tradition of AI Planning. Planning languages h ...