Advances in Dynamic Game Theory: Numerical Methods, by Thomas L. Vincent, Steffen Jørgensen, Marc Quincampoix

By Thomas L. Vincent, Steffen Jørgensen, Marc Quincampoix

This number of chosen contributions supplies an account of modern advancements in dynamic video game concept and its purposes, masking either theoretical advances and new functions of dynamic video games in such components as pursuit-evasion video games, ecology, and economics. Written through specialists of their respective disciplines, the chapters comprise stochastic and differential video games; dynamic video games and their functions in a number of components, corresponding to ecology and economics; pursuit-evasion video games; and evolutionary video game idea and functions. The paintings will function a state-of-the paintings account of contemporary advances in dynamic video game concept and its functions for researchers, practitioners, and complicated scholars in utilized arithmetic, mathematical finance, and engineering.

Show description

Read Online or Download Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games, Volume 9) PDF

Best game theory books

The Mathematics of Games (Recreations in Mathematics)

How nice a task does likelihood play in ball video games? Is it relatively a bonus to bluff at poker? What are the foundations at the back of non-attacking queens in chess, and the defective coin between twelve? What mathematical theories underlie video games of natural ability, and what primary paradoxes of arithmetic are delivered to gentle in the event you examine uncomplicated computerized video games?

Introduction to Maple For Mathematics Students

This direction is a laboratory within the use of the Maple machine arithmetic application to domathematics. With the arrival of quickly and inexpensive desktops, courses like Maple will exchange hand calculators and mathematical handbooks (like imperative tables) for many arithmetic scholars. arithmetic departments have already obvious this taking place in a slightly random and unplanned approach, so this direction was once invented to supply scholars with an creation to using this robust software.

Game Theory and the Social Contract, Vol. 2: Just Playing (Economic Learning and Social Evolution)

In quantity 1 of online game concept and the Social agreement, Ken Binmore restated the issues of ethical and political philosophy within the language of video game conception. In quantity 2, simply enjoying, he unveils his personal arguable conception, which abandons the metaphysics of Immanuel Kant for the naturalistic method of morality of David Hume.

Theory of Conditional Games

Online game conception explains the best way to make stable offerings whilst assorted choice makers have conflicting pursuits. The classical technique assumes that call makers are devoted to creating the simplest offerings for themselves whatever the impact on others, yet such an strategy is much less applicable while cooperation, compromise, and negotiation are very important.

Additional resources for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games, Volume 9)

Example text

We denote by A(x0 ) the set of VR-strategies for Ursula at x0 . A VR-strategy for Victor at initial condition x0 = (y0 , z0 ) is defined symmetrically as a map B : SG,P (y0 ) −→ SH,Q (z0 ) such that for any θ > 0, and for any trajectories y(·) and y(·) ˜ of SG,P (y0 ) which coincide on [0, θ ], the trajectories z(·) = B(y(·)) and z˜ (·) = B(y(·)) ˜ coincide on [0, θ ]. We denote by B(x0 ) the set of VR-strategies for Victor at x0 . We define, for all x = (y, z) ∈ Rn and all D ⊂ Rn closed, the functions H(x, D) := sup π ∈NPD (x) sup inf f (x, u, v), π u∈U v∈V , LV (x, D) := inf χD (y, q(z, ν)), (26) ν∈N LU V (x, D) := sup inf χD (p(y, µ), z), inf χD (p(y, µ), q(z, ν)) , ν∈N µ∈M (25) (27) where f (x, u, v) = f ((y, z), u, v) = (g(y, u), h(z, v)), and χD (·) denotes the characteristic function of the set D: χD (x) = 0 if x ∈ D +∞ otherwise.

The variations of price S(t) of assets at date t help find the variations Wπ(·) (t) of capital as a function of a strategy π(·) of the replicating portfolio. Indeed, the value of the replicating portfolio is given by Wπ (t) := π0 (t)S0 (t) + π1 (t)S1 (t). The self-financing principle of the portfolio reads ∀ t ≥ 0, π (t), S(t) = π0 (t)S0 (t) + π1 (t)S1 (t) = 0 so that the value of the portfolio satisfies W (t) = π(t), S (t) = π0 (t)S0 (t)γ0 (S(t)) + π1 (t)S1 (t)γ1 (S1 (t), v(t)), which is W (t) = W (t)γ0 (S(t)) − π1 (t)S1 (t)(γ0 (S0 (t)) − γ1 (S1 (t), v(t))).

Differential Games Through Viability Theory 13 We now introduce the notion of admissible controls and strategies. For an initial position (y0 , z0 ) ∈ KU × KV , U(y0 ) = {u(·) : [0, +∞) → U measurable | y[y0 , u(·)](t) ∈ KU ∀t ≥ 0} and V(z0 ) = {v(·) : [0, +∞) → V measurable | z[z0 , v(·)](t) ∈ KV ∀t ≥ 0}. Under the assumptions (9), it is well known that there are admissible controls for any initial position: namely, U(y0 ) = ∅ and V(z0 ) = ∅ ∀x0 = (y0 , z0 ) ∈ KU × KV . For any y ∈ KU , we set U (y) = U if y ∈ Int(KU ), U (y) = {u ∈ U | g(y, u) ∈ TKU (y)} if y ∈ ∂KU , where TKU (y) is the tangent half-space to the set KU at y ∈ ∂KU .

Download PDF sample

Rated 4.46 of 5 – based on 47 votes